Intermediate Algebra, Chapter 5, 5.1, Section 5.1, Problem 99

Simplify the expression $(5a^{-1})^4(a^2)^{-3}$ so that no negative exponents appear in the final result. Assume that the variables represent nonzero real numbers.

Remove the negative exponent in the numerator by rewriting $5a^{−1}$ as $\dfrac{5}{a}$. A negative exponent follows the rule: $a^{−n}= \dfrac{1}{a^n}$.

$ \left(\dfrac{5}{a} \right)^4(a^2)^{−3}$


Multiply $2$ by $3$ to get $6$.

$\dfrac{1}{a^6} \cdot \left(\dfrac{5}{a} \right)^4$


Raising a number to the $4$th power is the same as multiplying the number by itself $4$ times. In this case, $5$ raised to the $4$th power is $625$.

$\dfrac{1}{a^6} \cdot \dfrac{625}{a^4}$


Multiply $\dfrac{1}{a^6}$ by $\dfrac{625}{a^4}$ to get $\dfrac{625}{a^{10}}$.

$\dfrac{625}{a^{10}}$