Solve (-125)^frac{2{3}}*32^frac{2{5}}+[(-1)^frac{4{7}}]^frac{7{4}}=

$$( - 125 ) ^ { \frac { 2 } { 3 } } \times 32 ^ { \frac { 2 } { 5 } } + [ ( - 1 ) ^ { \frac { 4 } { 7 } } ] ^ { \frac { 7 } { 4 } } =$$

Evaluate

$$101$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{4}{7} and \frac{7}{4} to get 1.

$$\left(-125\right)^{\frac{2}{3}}\times 32^{\frac{2}{5}}+\left(-1\right)^{1}$$

Calculate -125 to the power of \frac{2}{3} and get 25.

$$25\times 32^{\frac{2}{5}}+\left(-1\right)^{1}$$

Calculate 32 to the power of \frac{2}{5} and get 4.

$$25\times 4+\left(-1\right)^{1}$$

Multiply 25 and 4 to get 100.

$$100+\left(-1\right)^{1}$$

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

$$100-1$$

Subtract 1 from 100 to get 99.

$$99$$

Factor

$$101$$