Pre-Algebra Examples

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Apply the product rule to $4 y$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $2$ .

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