Algebra Examples

$\frac{{(- 2 m^{4})}^{2}}{8 m^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $- 2 m^{4}$ .

$\frac{{(- 2)}^{2} {(m^{4})}^{2}}{8 m^{2}}$

Step 1.2

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

$\frac{4 {(m^{4})}^{2}}{8 m^{2}}$

Step 1.3

Multiply the exponents in ${(m^{4})}^{2}$ .

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Step 1.3.1

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

$\frac{4 m^{4 \cdot 2}}{8 m^{2}}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{4 m^{8}}{8 m^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $4 m^{8}$ .

$\frac{4 (m^{8})}{8 m^{2}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $4$ out of $8 m^{2}$ .

$\frac{4 (m^{8})}{4 (2 m^{2})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{4 m^{8}}{4 (2 m^{2})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{m^{8}}{2 m^{2}}$

Step 2.2

Cancel the common factor of $m^{8}$ and $m^{2}$ .

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Step 2.2.1

Factor $m^{2}$ out of $m^{8}$ .

$\frac{m^{2} m^{6}}{2 m^{2}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

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

$\frac{m^{2} m^{6}}{m^{2} \cdot 2}$

Step 2.2.2.2

Cancel the common factor.

$\frac{m^{2} m^{6}}{m^{2} \cdot 2}$

Step 2.2.2.3

Rewrite the expression.

$\frac{m^{6}}{2}$