Algebra Examples

${(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 1

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

${(\frac{y^{2}}{5 x y^{- 8} x^{4}})}^{3}$

Step 2

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 2.1

Move $x^{4}$ .

${(\frac{y^{2}}{5 (x^{4} x) y^{- 8}})}^{3}$

Step 2.2

Multiply $x^{4}$ by $x$ .

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Step 2.2.1

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

${(\frac{y^{2}}{5 (x^{4} x^{1}) y^{- 8}})}^{3}$

Step 2.2.2

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

${(\frac{y^{2}}{5 x^{4 + 1} y^{- 8}})}^{3}$

Step 2.3

Add $4$ and $1$ .

${(\frac{y^{2}}{5 x^{5} y^{- 8}})}^{3}$

Step 3

Move $y^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{y^{2} y^{8}}{5 x^{5}})}^{3}$

Step 4

Multiply $y^{2}$ by $y^{8}$ 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.

${(\frac{y^{2 + 8}}{5 x^{5}})}^{3}$

Step 4.2

Add $2$ and $8$ .

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

Step 5

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

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Step 5.1

Apply the product rule to $\frac{y^{10}}{5 x^{5}}$ .

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

Step 5.2

Apply the product rule to $5 x^{5}$ .

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

Step 6

Multiply the exponents in ${(y^{10})}^{3}$ .

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Step 6.1

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

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

Step 6.2

Multiply $10$ by $3$ .

$\frac{y^{30}}{5^{3} {(x^{5})}^{3}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $5$ to the power of $3$ .

$\frac{y^{30}}{125 {(x^{5})}^{3}}$

Step 7.2

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 7.2.1

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

$\frac{y^{30}}{125 x^{5 \cdot 3}}$

Step 7.2.2

Multiply $5$ by $3$ .

$\frac{y^{30}}{125 x^{15}}$