Pre-Algebra Examples

${(\frac{x^{- 3} y^{- 4}}{x^{- 5} y^{6}})}^{2}$

Step 1

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{x^{- 3}}{x^{- 5} y^{6} y^{4}})}^{2}$

Step 2

Multiply $y^{6}$ by $y^{4}$ by adding the exponents.

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Step 2.1

Move $y^{4}$ .

${(\frac{x^{- 3}}{x^{- 5} (y^{4} y^{6})})}^{2}$

Step 2.2

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

${(\frac{x^{- 3}}{x^{- 5} y^{4 + 6}})}^{2}$

Step 2.3

Add $4$ and $6$ .

${(\frac{x^{- 3}}{x^{- 5} y^{10}})}^{2}$

Step 3

Move $x^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{x^{- 3} x^{5}}{y^{10}})}^{2}$

Step 4

Multiply $x^{- 3}$ by $x^{5}$ by adding the exponents.

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Step 4.1

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

${(\frac{x^{- 3 + 5}}{y^{10}})}^{2}$

Step 4.2

Add $- 3$ and $5$ .

${(\frac{x^{2}}{y^{10}})}^{2}$

Step 5

Apply the product rule to $\frac{x^{2}}{y^{10}}$ .

$\frac{{(x^{2})}^{2}}{{(y^{10})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{x^{2 \cdot 2}}{{(y^{10})}^{2}}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{x^{4}}{{(y^{10})}^{2}}$

Step 7

Multiply the exponents in ${(y^{10})}^{2}$ .

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Step 7.1

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

$\frac{x^{4}}{y^{10 \cdot 2}}$

Step 7.2

Multiply $10$ by $2$ .

$\frac{x^{4}}{y^{20}}$