Algebra Examples

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

Step 1

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

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

Step 2

Combine $3$ and $\frac{1}{x^{4}}$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the numerator.

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Step 5.1

Raise $3$ to the power of $2$ .

$\frac{9 {(y^{3})}^{2}}{{(x^{4})}^{2}}$

Step 5.2

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

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Step 5.2.1

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

$\frac{9 y^{3 \cdot 2}}{{(x^{4})}^{2}}$

Step 5.2.2

Multiply $3$ by $2$ .

$\frac{9 y^{6}}{{(x^{4})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{9 y^{6}}{x^{4 \cdot 2}}$

Step 6.2

Multiply $4$ by $2$ .

$\frac{9 y^{6}}{x^{8}}$