Intermediate Algebra, Chapter 5, 5.1, Section 5.1, Problem 100

Simplify the expression $(3p^{-4})^2(p^3)^{-1}$ 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 $3p^{−4}$ as $\dfrac{3}{p^4}$. A negative exponent follows the rule: $a^{−n}= \dfrac{1}{a^n}$.

$ \left(\dfrac{3}{p^4} \right)^2(p^3)^{−1}$


Multiply $3$ by $1$ to get $3$.

$\dfrac{1}{p^3} \cdot \left(\dfrac{3}{p^4} \right)^2$


Raising a number to the $2$nd power is the same as multiplying the number by itself $2$ times. In this case, $\dfrac{3}{p^4}$ raised to the $2$nd power is $\dfrac{9}{p^8}$.

$\dfrac{1}{p^3} \cdot \dfrac{9}{p^8}$


Multiply $\dfrac{1}{p^3}$ by $\dfrac{9}{p^8}$ to get $\dfrac{9}{p^{11}}$.

$\dfrac{9}{p^{11}}$