Simplify (2(p^2)^-4)/(2r^-2)

$\frac{2 {(p^{2})}^{- 4}}{2 r^{- 2}}$

Step 1

Simplify.

Move ${(p^{2})}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2}{2 r^{- 2} {(p^{2})}^{4}}$

Move $r^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 r^{2}}{2 {(p^{2})}^{4}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 r^{2}}{2 {(p^{2})}^{4}}$

Rewrite the expression.

$\frac{r^{2}}{{(p^{2})}^{4}}$

Step 3

Multiply the exponents in ${(p^{2})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{r^{2}}{p^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{r^{2}}{p^{8}}$