Solve [a][{(-1/5)^-2}^2]^-1quad[b]

$$[ a ] [ \{ ( \frac { - 1 } { 5 } ) ^ { - 2 } \} ^ { 2 } ] ^ { - 1 } \quad [ b ]$$

Evaluate

$$\frac{ab}{625}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$a\times \left(\left(\frac{-1}{5}\right)^{-4}\right)^{-1}b$$

To raise a power to another power, multiply the exponents. Multiply -4 and -1 to get 4.

$$a\times \left(\frac{-1}{5}\right)^{4}b$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$a\left(-\frac{1}{5}\right)^{4}b$$

Calculate -\frac{1}{5} to the power of 4 and get \frac{1}{625}.

$$a\times \frac{1}{625}b$$

Differentiate w.r.t. a

$$\frac{b}{625}$$