Algebra Examples

${(\frac{3 x^{- 1} y^{- 6}}{9 x^{5} y^{- 2}})}^{- 1}$

Step 1

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{3 y^{- 6}}{9 x^{5} y^{- 2} x})}^{- 1}$

Step 2

Move $y^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{3}{9 x^{5} y^{- 2} x y^{6}})}^{- 1}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $x^{5}$ by $x$ by adding the exponents.

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Step 3.1.1

Move $x$ .

${(\frac{3}{9 (x \cdot x^{5}) y^{- 2} y^{6}})}^{- 1}$

Step 3.1.2

Multiply $x$ by $x^{5}$ .

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Step 3.1.2.1

Raise $x$ to the power of $1$ .

${(\frac{3}{9 (x^{1} x^{5}) y^{- 2} y^{6}})}^{- 1}$

Step 3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{3}{9 x^{1 + 5} y^{- 2} y^{6}})}^{- 1}$

Step 3.1.3

Add $1$ and $5$ .

${(\frac{3}{9 x^{6} y^{- 2} y^{6}})}^{- 1}$

Step 3.2

Multiply $y^{- 2}$ by $y^{6}$ by adding the exponents.

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Step 3.2.1

Move $y^{6}$ .

${(\frac{3}{9 x^{6} (y^{6} y^{- 2})})}^{- 1}$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{3}{9 x^{6} y^{6 - 2}})}^{- 1}$

Step 3.2.3

Subtract $2$ from $6$ .

${(\frac{3}{9 x^{6} y^{4}})}^{- 1}$

Step 4

Cancel the common factor of $3$ and $9$ .

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Step 4.1

Factor $3$ out of $3$ .

${(\frac{3 (1)}{9 x^{6} y^{4}})}^{- 1}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $9 x^{6} y^{4}$ .

${(\frac{3 (1)}{3 (3 x^{6} y^{4})})}^{- 1}$

Step 4.2.2

Cancel the common factor.

${(\frac{3 \cdot 1}{3 (3 x^{6} y^{4})})}^{- 1}$

Step 4.2.3

Rewrite the expression.

${(\frac{1}{3 x^{6} y^{4}})}^{- 1}$

Step 5

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

$3 x^{6} y^{4}$