Simplify (7uv^2)^-5

${(7 u v^{2})}^{- 5}$

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

$\frac{1}{{(7 u v^{2})}^{5}}$

Simplify the denominator.

Apply the product rule to $7 u v^{2}$ .

$\frac{1}{{(7 u)}^{5} {(v^{2})}^{5}}$

Apply the product rule to $7 u$ .

$\frac{1}{7^{5} u^{5} {(v^{2})}^{5}}$

Raise $7$ to the power of $5$ .

$\frac{1}{16807 u^{5} {(v^{2})}^{5}}$

Multiply the exponents in ${(v^{2})}^{5}$ .

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

$\frac{1}{16807 u^{5} v^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{1}{16807 u^{5} v^{10}}$