Solve {l}{2^{4}-2(2)^{3}-3(2)^{8}+7(2)-10}{[-3(-1)^{3}-4(-2)^{2}]^{2}}{4(0,1)^{2}-6(0,1)+(0,7)-(0,1)^{3}}{4(1/3)^{4}+3(1/3)^{2}+2(1/3)+7}{3(-3)^{3}+4(-3)^{4}-5(-3)^2+12}{[-4(-2)^4+5(-2)^9-3(-2)+2]^3}

$$\left. \begin{array} { l } { 2 ^ { 4 } - 2 ( 2 ) ^ { 3 } - 3 ( 2 ) ^ { 8 } + 7 ( 2 ) - 10 } \\ { [ - 3 ( - 1 ) ^ { 3 } - 4 ( - 2 ) ^ { 2 } ] ^ { 2 } } \\ { 4 ( 0,1 ) ^ { 2 } - 6 ( 0,1 ) + ( 0,7 ) - ( 0,1 ) ^ { 3 } } \\ { 4 ( \frac { 1 } { 3 } ) ^ { 4 } + 3 ( \frac { 1 } { 3 } ) ^ { 2 } + 2 ( \frac { 1 } { 3 } ) + 7 } \\ { 3 ( - 3 ) ^ { 3 } + 4 ( - 3 ) ^ { 4 } - 5 ( - 3 ) ^ { 2 } + 12 } \\ { [ - 4 ( - 2 ) ^ { 4 } + 5 ( - 2 ) ^ { 9 } - 3 ( - 2 ) + 2 ] ^ { 3 } } \end{array} \right.$$

Sort

$$-17902480896;-764;0,139;\frac{652}{81};169;210$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$sort(2^{4}-2^{4}-3\times 2^{8}+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate 2 to the power of 4 and get 16.

$$sort(16-2^{4}-3\times 2^{8}+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate 2 to the power of 4 and get 16.

$$sort(16-16-3\times 2^{8}+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 16 from 16 to get 0.

$$sort(0-3\times 2^{8}+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate 2 to the power of 8 and get 256.

$$sort(0-3\times 256+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 3 and 256 to get 768.

$$sort(0-768+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 768 from 0 to get -768.

$$sort(-768+7\times 2-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 7 and 2 to get 14.

$$sort(-768+14-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add -768 and 14 to get -754.

$$sort(-754-10;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 10 from -754 to get -764.

$$sort(-764;\left(-3\left(-1\right)^{3}-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -1 to the power of 3 and get -1.

$$sort(-764;\left(-3\left(-1\right)-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply -3 and -1 to get 3.

$$sort(-764;\left(3-4\left(-2\right)^{2}\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -2 to the power of 2 and get 4.

$$sort(-764;\left(3-4\times 4\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 4 and 4 to get 16.

$$sort(-764;\left(3-16\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 16 from 3 to get -13.

$$sort(-764;\left(-13\right)^{2};4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -13 to the power of 2 and get 169.

$$sort(-764;169;4\times 0,1^{2}-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate 0,1 to the power of 2 and get 0,01.

$$sort(-764;169;4\times 0,01-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 4 and 0,01 to get 0,04.

$$sort(-764;169;0,04-6\times 0,1+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 6 and 0,1 to get 0,6.

$$sort(-764;169;0,04-0,6+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 0,6 from 0,04 to get -0,56.

$$sort(-764;169;-0,56+0,7-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add -0,56 and 0,7 to get 0,14.

$$sort(-764;169;0,14-0,1^{3};4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate 0,1 to the power of 3 and get 0,001.

$$sort(-764;169;0,14-0,001;4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 0,001 from 0,14 to get 0,139.

$$sort(-764;169;0,139;4\times \left(\frac{1}{3}\right)^{4}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate \frac{1}{3} to the power of 4 and get \frac{1}{81}.

$$sort(-764;169;0,139;4\times \frac{1}{81}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 4 and \frac{1}{81} to get \frac{4}{81}.

$$sort(-764;169;0,139;\frac{4}{81}+3\times \left(\frac{1}{3}\right)^{2}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$sort(-764;169;0,139;\frac{4}{81}+3\times \frac{1}{9}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 3 and \frac{1}{9} to get \frac{1}{3}.

$$sort(-764;169;0,139;\frac{4}{81}+\frac{1}{3}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add \frac{4}{81} and \frac{1}{3} to get \frac{31}{81}.

$$sort(-764;169;0,139;\frac{31}{81}+2\times \frac{1}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$sort(-764;169;0,139;\frac{31}{81}+\frac{2}{3}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add \frac{31}{81} and \frac{2}{3} to get \frac{85}{81}.

$$sort(-764;169;0,139;\frac{85}{81}+7;3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add \frac{85}{81} and 7 to get \frac{652}{81}.

$$sort(-764;169;0,139;\frac{652}{81};3\left(-3\right)^{3}+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -3 to the power of 3 and get -27.

$$sort(-764;169;0,139;\frac{652}{81};3\left(-27\right)+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 3 and -27 to get -81.

$$sort(-764;169;0,139;\frac{652}{81};-81+4\left(-3\right)^{4}-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -3 to the power of 4 and get 81.

$$sort(-764;169;0,139;\frac{652}{81};-81+4\times 81-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 4 and 81 to get 324.

$$sort(-764;169;0,139;\frac{652}{81};-81+324-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add -81 and 324 to get 243.

$$sort(-764;169;0,139;\frac{652}{81};243-5\left(-3\right)^{2}+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -3 to the power of 2 and get 9.

$$sort(-764;169;0,139;\frac{652}{81};243-5\times 9+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply 5 and 9 to get 45.

$$sort(-764;169;0,139;\frac{652}{81};243-45+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Subtract 45 from 243 to get 198.

$$sort(-764;169;0,139;\frac{652}{81};198+12;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Add 198 and 12 to get 210.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-4\left(-2\right)^{4}+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -2 to the power of 4 and get 16.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-4\times 16+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Multiply -4 and 16 to get -64.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-64+5\left(-2\right)^{9}-3\left(-2\right)+2\right)^{3})$$

Calculate -2 to the power of 9 and get -512.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-64+5\left(-512\right)-3\left(-2\right)+2\right)^{3})$$

Multiply 5 and -512 to get -2560.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-64-2560-3\left(-2\right)+2\right)^{3})$$

Subtract 2560 from -64 to get -2624.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-2624-3\left(-2\right)+2\right)^{3})$$

Multiply 3 and -2 to get -6.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-2624-\left(-6\right)+2\right)^{3})$$

The opposite of -6 is 6.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-2624+6+2\right)^{3})$$

Add -2624 and 6 to get -2618.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-2618+2\right)^{3})$$

Add -2618 and 2 to get -2616.

$$sort(-764;169;0,139;\frac{652}{81};210;\left(-2616\right)^{3})$$

Calculate -2616 to the power of 3 and get -17902480896.

$$sort(-764;169;0,139;\frac{652}{81};210;-17902480896)$$

Convert decimal numbers in the list -764;169;0,139;\frac{652}{81};210;-17902480896 to fractions.

$$-764;169;\frac{139}{1000};\frac{652}{81};210;-17902480896$$

Least common denominator of the numbers in the list -764;169;\frac{139}{1000};\frac{652}{81};210;-17902480896 is 81000. Convert numbers in the list to fractions with denominator 81000.

$$-\frac{61884000}{81000};\frac{13689000}{81000};\frac{11259}{81000};\frac{652000}{81000};\frac{17010000}{81000};-\frac{1450100952576000}{81000}$$

To sort the list, start from a single element -\frac{61884000}{81000}.

$$-\frac{61884000}{81000}$$

Insert \frac{13689000}{81000} to the appropriate location in the new list.

$$-\frac{61884000}{81000};\frac{13689000}{81000}$$

Insert \frac{11259}{81000} to the appropriate location in the new list.

$$-\frac{61884000}{81000};\frac{11259}{81000};\frac{13689000}{81000}$$

Insert \frac{652000}{81000} to the appropriate location in the new list.

$$-\frac{61884000}{81000};\frac{11259}{81000};\frac{652000}{81000};\frac{13689000}{81000}$$

Insert \frac{17010000}{81000} to the appropriate location in the new list.

$$-\frac{61884000}{81000};\frac{11259}{81000};\frac{652000}{81000};\frac{13689000}{81000};\frac{17010000}{81000}$$

Insert -\frac{1450100952576000}{81000} to the appropriate location in the new list.

$$-\frac{1450100952576000}{81000};-\frac{61884000}{81000};\frac{11259}{81000};\frac{652000}{81000};\frac{13689000}{81000};\frac{17010000}{81000}$$

Replace the obtained fractions with the initial values.

$$-17902480896;-764;0,139;\frac{652}{81};169;210$$

Evaluate

$$-764,\ 169,\ 0,139,\ \frac{652}{81},\ 210,\ -17902480896$$