Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $- 2$ .

$\frac{y^{2}}{x^{3}} y^{- 6}$

Step 4

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

$\frac{y^{2}}{x^{3}} \cdot \frac{1}{y^{6}}$

Step 5

Combine.

$\frac{y^{2} \cdot 1}{x^{3} y^{6}}$

Step 6

Cancel the common factor of $y^{2}$ and $y^{6}$ .

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Step 6.1

Factor $y^{2}$ out of $y^{2} \cdot 1$ .

$\frac{y^{2} (1)}{x^{3} y^{6}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{2}$ out of $x^{3} y^{6}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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