Solve {l}{1/4+0,19:(4-0,8:0,5-1/2)}{(1/2)^-4*1/2(4-1)^2+(-1)^0}

$$\left. \begin{array} { l } { \frac { 1 } { 4 } + 0,19 : ( 4 - 0,8 : 0,5 - \frac { 1 } { 2 } ) } \\ { ( \frac { 1 } { 2 } ) ^ { - 4 } \cdot \frac { 1 } { 2 } ( 4 - 1 ) ^ { 2 } + ( - 1 ) ^ { 0 } } \end{array} \right.$$

Sort

$$0,35,\ 73$$

Solution Steps

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

$$sort(\frac{1}{4}+\frac{0,19}{4-\frac{0,8}{0,5}-\frac{1}{2}};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Expand \frac{0,8}{0,5} by multiplying both numerator and the denominator by 10.

$$sort(\frac{1}{4}+\frac{0,19}{4-\frac{8}{5}-\frac{1}{2}};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Subtract \frac{8}{5} from 4 to get \frac{12}{5}.

$$sort(\frac{1}{4}+\frac{0,19}{\frac{12}{5}-\frac{1}{2}};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Subtract \frac{1}{2} from \frac{12}{5} to get \frac{19}{10}.

$$sort(\frac{1}{4}+\frac{0,19}{\frac{19}{10}};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Divide 0,19 by \frac{19}{10} by multiplying 0,19 by the reciprocal of \frac{19}{10}.

$$sort(\frac{1}{4}+0,19\times \frac{10}{19};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Multiply 0,19 and \frac{10}{19} to get \frac{1}{10}.

$$sort(\frac{1}{4}+\frac{1}{10};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Add \frac{1}{4} and \frac{1}{10} to get \frac{7}{20}.

$$sort(\frac{7}{20};\left(\frac{1}{2}\right)^{-3}\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Calculate \frac{1}{2} to the power of -3 and get 8.

$$sort(\frac{7}{20};8\left(4-1\right)^{2}+\left(-1\right)^{0})$$

Subtract 1 from 4 to get 3.

$$sort(\frac{7}{20};8\times 3^{2}+\left(-1\right)^{0})$$

Calculate 3 to the power of 2 and get 9.

$$sort(\frac{7}{20};8\times 9+\left(-1\right)^{0})$$

Multiply 8 and 9 to get 72.

$$sort(\frac{7}{20};72+\left(-1\right)^{0})$$

Calculate -1 to the power of 0 and get 1.

$$sort(\frac{7}{20};72+1)$$

Add 72 and 1 to get 73.

$$sort(\frac{7}{20};73)$$

Convert decimal numbers in the list \frac{7}{20};73 to fractions.

$$\frac{7}{20};73$$

Evaluate

$$0,35,\ 73$$