Algebra Examples

$\frac{4 w^{- 3} {(2 q)}^{2}}{8 w^{2} q^{3}}$

Step 1

Move $w^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 {(2 q)}^{2}}{8 w^{2} q^{3} w^{3}}$

Step 2

Multiply $w^{2}$ by $w^{3}$ by adding the exponents.

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Step 2.1

Move $w^{3}$ .

$\frac{4 {(2 q)}^{2}}{8 (w^{3} w^{2}) q^{3}}$

Step 2.2

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

$\frac{4 {(2 q)}^{2}}{8 w^{3 + 2} q^{3}}$

Step 2.3

Add $3$ and $2$ .

$\frac{4 {(2 q)}^{2}}{8 w^{5} q^{3}}$

Step 3

Cancel the common factor of $4$ and $8$ .

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Step 3.1

Factor $4$ out of $4 {(2 q)}^{2}$ .

$\frac{4 ({(2 q)}^{2})}{8 w^{5} q^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $8 w^{5} q^{3}$ .

$\frac{4 ({(2 q)}^{2})}{4 (2 w^{5} q^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{4 {(2 q)}^{2}}{4 (2 w^{5} q^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{{(2 q)}^{2}}{2 w^{5} q^{3}}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the product rule to $2 q$ .

$\frac{2^{2} q^{2}}{2 w^{5} q^{3}}$

Step 4.2

Raise $2$ to the power of $2$ .

$\frac{4 q^{2}}{2 w^{5} q^{3}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $4$ and $2$ .

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Step 5.1.1

Factor $2$ out of $4 q^{2}$ .

$\frac{2 (2 q^{2})}{2 w^{5} q^{3}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $2$ out of $2 w^{5} q^{3}$ .

$\frac{2 (2 q^{2})}{2 (w^{5} q^{3})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{2 (2 q^{2})}{2 (w^{5} q^{3})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{2 q^{2}}{w^{5} q^{3}}$

Step 5.2

Cancel the common factor of $q^{2}$ and $q^{3}$ .

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Step 5.2.1

Factor $q^{2}$ out of $2 q^{2}$ .

$\frac{q^{2} \cdot 2}{w^{5} q^{3}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $q^{2}$ out of $w^{5} q^{3}$ .

$\frac{q^{2} \cdot 2}{q^{2} (w^{5} q)}$

Step 5.2.2.2

Cancel the common factor.

$\frac{q^{2} \cdot 2}{q^{2} (w^{5} q)}$

Step 5.2.2.3

Rewrite the expression.

$\frac{2}{w^{5} q}$