Solve {l}{5^{0}+6^{1}*(6^{2}*6^{3}:6^{4}+2^{3})+5-8^{2}-2^{3}}{3^{2}:3+4^{2}:4^2+(5^2*2-50):2^2-3^3}

$$\left. \begin{array} { l } { 5 ^ { 0 } + 6 ^ { 1 } \cdot ( 6 ^ { 2 } \cdot 6 ^ { 3 } : 6 ^ { 4 } + 2 ^ { 3 } ) + 5 - 8 ^ { 2 } - 2 ^ { 3 } } \\ { 3 ^ { 2 } : 3 + 4 ^ { 2 } : 4 ^ { 2 } + ( 5 ^ { 2 } \cdot 2 - 50 ) : 2 ^ { 2 } - 3 ^ { 3 } } \end{array} \right.$$

Sort

$$-23,18$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$sort(5^{0}+6^{1}\left(\frac{6^{5}}{6^{4}}+2^{3}\right)+5-8^{2}-2^{3},\frac{3^{2}}{3}+\frac{4^{2}}{4^{2}}+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$sort(5^{0}+6^{1}\left(6^{1}+2^{3}\right)+5-8^{2}-2^{3},\frac{3^{2}}{3}+\frac{4^{2}}{4^{2}}+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$sort(5^{0}+6^{1}\left(6^{1}+2^{3}\right)+5-8^{2}-2^{3},3^{1}+\frac{4^{2}}{4^{2}}+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Divide 4^{2} by 4^{2} to get 1.

$$sort(5^{0}+6^{1}\left(6^{1}+2^{3}\right)+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 5 to the power of 0 and get 1.

$$sort(1+6^{1}\left(6^{1}+2^{3}\right)+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 6 to the power of 1 and get 6.

$$sort(1+6\left(6^{1}+2^{3}\right)+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 6 to the power of 1 and get 6.

$$sort(1+6\left(6+2^{3}\right)+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 2 to the power of 3 and get 8.

$$sort(1+6\left(6+8\right)+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Add 6 and 8 to get 14.

$$sort(1+6\times 14+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Multiply 6 and 14 to get 84.

$$sort(1+84+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Add 1 and 84 to get 85.

$$sort(85+5-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Add 85 and 5 to get 90.

$$sort(90-8^{2}-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 8 to the power of 2 and get 64.

$$sort(90-64-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Subtract 64 from 90 to get 26.

$$sort(26-2^{3},3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 2 to the power of 3 and get 8.

$$sort(26-8,3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Subtract 8 from 26 to get 18.

$$sort(18,3^{1}+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 3 to the power of 1 and get 3.

$$sort(18,3+1+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Add 3 and 1 to get 4.

$$sort(18,4+\frac{5^{2}\times 2-50}{2^{2}}-3^{3})$$

Calculate 5 to the power of 2 and get 25.

$$sort(18,4+\frac{25\times 2-50}{2^{2}}-3^{3})$$

Multiply 25 and 2 to get 50.

$$sort(18,4+\frac{50-50}{2^{2}}-3^{3})$$

Subtract 50 from 50 to get 0.

$$sort(18,4+\frac{0}{2^{2}}-3^{3})$$

Calculate 2 to the power of 2 and get 4.

$$sort(18,4+\frac{0}{4}-3^{3})$$

Zero divided by any non-zero number gives zero.

$$sort(18,4+0-3^{3})$$

Add 4 and 0 to get 4.

$$sort(18,4-3^{3})$$

Calculate 3 to the power of 3 and get 27.

$$sort(18,4-27)$$

Subtract 27 from 4 to get -23.

$$sort(18,-23)$$

To sort the list, start from a single element 18.

$$18$$

Insert -23 to the appropriate location in the new list.

$$-23,18$$

Evaluate

$$18,\ -23$$