Simplify (4x^3y^-1)^2

${(4 x^{3} y^{- 1})}^{2}$

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

${(4 x^{3} \frac{1}{y})}^{2}$

Multiply $4 x^{3} \frac{1}{y}$ .

Combine $4$ and $\frac{1}{y}$ .

${(x^{3} \frac{4}{y})}^{2}$

Combine $x^{3}$ and $\frac{4}{y}$ .

${(\frac{x^{3} \cdot 4}{y})}^{2}$

Move $4$ to the left of $x^{3}$ .

${(\frac{4 \cdot x^{3}}{y})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{4 x^{3}}{y}$ .

$\frac{{(4 x^{3})}^{2}}{y^{2}}$

Apply the product rule to $4 x^{3}$ .

$\frac{4^{2} {(x^{3})}^{2}}{y^{2}}$

Simplify the numerator.

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

$\frac{16 {(x^{3})}^{2}}{y^{2}}$

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

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

$\frac{16 x^{3 \cdot 2}}{y^{2}}$

Multiply $3$ by $2$ .

$\frac{16 x^{6}}{y^{2}}$