Algebra Examples

${(\frac{x^{0} y^{3}}{x^{- 2} y})}^{3}$

Step 1

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{x^{0} y^{3} x^{2}}{y})}^{3}$

Step 2

Multiply $x^{0}$ by $x^{2}$ by adding the exponents.

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Step 2.1

Move $x^{2}$ .

${(\frac{x^{2} x^{0} y^{3}}{y})}^{3}$

Step 2.2

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

${(\frac{x^{2 + 0} y^{3}}{y})}^{3}$

Step 2.3

Add $2$ and $0$ .

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

Step 3

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

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Step 3.1

Factor $y$ out of $x^{2} y^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Factor $y$ out of $y^{1}$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

Divide $x^{2} y^{2}$ by $1$ .

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

Step 4

Apply basic rules of exponents.

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Step 4.1

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

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $3$ .

$x^{6} {(y^{2})}^{3}$

Step 4.3

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

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Step 4.3.1

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

$x^{6} y^{2 \cdot 3}$

Step 4.3.2

Multiply $2$ by $3$ .

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