Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine.

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

Step 4

Multiply $1$ by $1$ .

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

Step 5

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

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

Step 6

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

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Multiply $2$ by $3$ .

$x^{6} y^{3}$