Finite Math Examples

$\frac{2 a^{2}}{{(- 4 a^{4})}^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{2 a^{2}}{{(- 4)}^{2} {(a^{4})}^{2}}$

Step 1.2

Raise $- 4$ to the power of $2$ .

$\frac{2 a^{2}}{16 {(a^{4})}^{2}}$

Step 1.3

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

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Step 1.3.1

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

$\frac{2 a^{2}}{16 a^{4 \cdot 2}}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{2 a^{2}}{16 a^{8}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $2$ and $16$ .

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Step 2.1.1

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

$\frac{2 (a^{2})}{16 a^{8}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $16 a^{8}$ .

$\frac{2 (a^{2})}{2 (8 a^{8})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 a^{2}}{2 (8 a^{8})}$

Step 2.1.2.3

Rewrite the expression.

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

Step 2.2

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

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Step 2.2.1

Multiply by $1$ .

$\frac{a^{2} \cdot 1}{8 a^{8}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

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

$\frac{a^{2} \cdot 1}{a^{2} (8 a^{6})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{a^{2} \cdot 1}{a^{2} (8 a^{6})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{1}{8 a^{6}}$