Simplify (5w^-2)(4w)^-2

$(5 w^{- 2}) {(4 w)}^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$5 \frac{1}{w^{2}} {(4 w)}^{- 2}$

Combine $5$ and $\frac{1}{w^{2}}$ .

$\frac{5}{w^{2}} {(4 w)}^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5}{w^{2}} \cdot \frac{1}{{(4 w)}^{2}}$

Combine fractions.

Combine.

$\frac{5 \cdot 1}{w^{2} {(4 w)}^{2}}$

Multiply $5$ by $1$ .

$\frac{5}{w^{2} {(4 w)}^{2}}$

Simplify the denominator.

Apply the product rule to $4 w$ .

$\frac{5}{w^{2} \cdot 4^{2} w^{2}}$

Multiply $w^{2}$ by $w^{2}$ by adding the exponents.

Move $w^{2}$ .

$\frac{5}{w^{2} w^{2} \cdot 4^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5}{w^{2 + 2} \cdot 4^{2}}$

Add $2$ and $2$ .

$\frac{5}{w^{4} \cdot 4^{2}}$

Raise $4$ to the power of $2$ .

$\frac{5}{w^{4} \cdot 16}$

Move $16$ to the left of $w^{4}$ .

$\frac{5}{16 w^{4}}$