Solve [(-2/5)^3:(-2/5)^-2]^-1*(-2/5)^7=

$$[ ( - \frac { 2 } { 5 } ) ^ { 3 } : ( - \frac { 2 } { 5 } ) ^ { - 2 } ] ^ { - 1 } \cdot ( - \frac { 2 } { 5 } ) ^ { 7 } =$$

Evaluate

$$\frac{4}{25}=0.16$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 3 to get 5.

$$\left(\left(-\frac{2}{5}\right)^{5}\right)^{-1}\left(-\frac{2}{5}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -1 to get -5.

$$\left(-\frac{2}{5}\right)^{-5}\left(-\frac{2}{5}\right)^{7}$$

To multiply powers of the same base, add their exponents. Add -5 and 7 to get 2.

$$\left(-\frac{2}{5}\right)^{2}$$

Calculate -\frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{4}{25}$$

Factor

$$\frac{2 ^ {2}}{5 ^ {2}} = 0.16$$