Simplify (7z^3)^-2y

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

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

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

Simplify the denominator.

Apply the product rule to $7 z^{3}$ .

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

Raise $7$ to the power of $2$ .

$\frac{1}{49 {(z^{3})}^{2}} y$

Multiply the exponents in ${(z^{3})}^{2}$ .

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

$\frac{1}{49 z^{3 \cdot 2}} y$

Multiply $3$ by $2$ .

$\frac{1}{49 z^{6}} y$

Combine $\frac{1}{49 z^{6}}$ and $y$ .

$\frac{y}{49 z^{6}}$