Simplify (3y^7)/((2y^-2)^-5)

$\frac{3 y^{7}}{{(2 y^{- 2})}^{- 5}}$

Move ${(2 y^{- 2})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3 y^{7} {(2 y^{- 2})}^{5}$

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

$3 y^{7} {(2 \frac{1}{y^{2}})}^{5}$

Combine $2$ and $\frac{1}{y^{2}}$ .

$3 y^{7} {(\frac{2}{y^{2}})}^{5}$

Simplify the expression.

Apply the product rule to $\frac{2}{y^{2}}$ .

$3 y^{7} \frac{2^{5}}{{(y^{2})}^{5}}$

Raise $2$ to the power of $5$ .

$3 y^{7} \frac{32}{{(y^{2})}^{5}}$

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

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

$3 y^{7} \frac{32}{y^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$3 y^{7} \frac{32}{y^{10}}$

Cancel the common factor of $y^{7}$ .

Factor $y^{7}$ out of $3 y^{7}$ .

$y^{7} \cdot 3 \frac{32}{y^{10}}$

Factor $y^{7}$ out of $y^{10}$ .

$y^{7} \cdot 3 \frac{32}{y^{7} y^{3}}$

Cancel the common factor.

$y^{7} \cdot 3 \frac{32}{y^{7} y^{3}}$

Rewrite the expression.

$3 \frac{32}{y^{3}}$

Combine $3$ and $\frac{32}{y^{3}}$ .

$\frac{3 \cdot 32}{y^{3}}$

Multiply $3$ by $32$ .

$\frac{96}{y^{3}}$