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

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

Step 1

Move $y^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

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

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

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

Add $2$ and $1$ .

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

Step 3

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

Apply the product rule to $\frac{2 x^{3}}{y^{3}}$ .

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

Apply the product rule to $2 x^{3}$ .

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

Step 4

Simplify the numerator.

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

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

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

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

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

Multiply $3$ by $2$ .

$\frac{4 x^{6}}{{(y^{3})}^{2}}$

Step 5

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

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

$\frac{4 x^{6}}{y^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{4 x^{6}}{y^{6}}$