Pre-Algebra Examples

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

Step 1

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

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

Step 2

Combine $3$ and $\frac{1}{x^{2}}$ .

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

Step 3

Combine $\frac{3}{x^{2}}$ and $y^{3}$ .

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Apply the product rule to $3 y^{3}$ .

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

Step 6

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $4$ .

$\frac{x^{8}}{3^{4} {(y^{3})}^{4}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $3$ to the power of $4$ .

$\frac{x^{8}}{81 {(y^{3})}^{4}}$

Step 7.2

Multiply the exponents in ${(y^{3})}^{4}$ .

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Step 7.2.1

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

$\frac{x^{8}}{81 y^{3 \cdot 4}}$

Step 7.2.2

Multiply $3$ by $4$ .

$\frac{x^{8}}{81 y^{12}}$