Algebra Examples

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

Step 1

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

${(\frac{x^{4} y \cdot y^{5}}{x^{3}})}^{3}$

Step 2

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

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Step 2.1

Move $y^{5}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $5$ and $1$ .

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

Step 3

Cancel the common factor of $x^{4}$ and $x^{3}$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $x y^{6}$ by $1$ .

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

Step 4

Apply basic rules of exponents.

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Step 4.1

Apply the product rule to $x y^{6}$ .

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

Step 4.2

Multiply the exponents in ${(y^{6})}^{3}$ .

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Step 4.2.1

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

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

Step 4.2.2

Multiply $6$ by $3$ .

$x^{3} y^{18}$