Algebra Examples

$\frac{{(16 x^{- 4})}^{2}}{{(4 x^{- 2})}^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $16 x^{- 4}$ .

$\frac{16^{2} {(x^{- 4})}^{2}}{{(4 x^{- 2})}^{3}}$

Step 1.2

Raise $16$ to the power of $2$ .

$\frac{256 {(x^{- 4})}^{2}}{{(4 x^{- 2})}^{3}}$

Step 1.3

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

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Step 1.3.1

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

$\frac{256 x^{- 4 \cdot 2}}{{(4 x^{- 2})}^{3}}$

Step 1.3.2

Multiply $- 4$ by $2$ .

$\frac{256 x^{- 8}}{{(4 x^{- 2})}^{3}}$

Step 1.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{256 \frac{1}{x^{8}}}{{(4 x^{- 2})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{256 \frac{1}{x^{8}}}{4^{3} {(x^{- 2})}^{3}}$

Step 2.2

Raise $4$ to the power of $3$ .

$\frac{256 \frac{1}{x^{8}}}{64 {(x^{- 2})}^{3}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{256 \frac{1}{x^{8}}}{64 x^{- 2 \cdot 3}}$

Step 2.3.2

Multiply $- 2$ by $3$ .

$\frac{256 \frac{1}{x^{8}}}{64 x^{- 6}}$

Step 2.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{256 \frac{1}{x^{8}}}{64 \frac{1}{x^{6}}}$

Step 3

Combine fractions.

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Step 3.1

Combine $256$ and $\frac{1}{x^{8}}$ .

$\frac{\frac{256}{x^{8}}}{64 \frac{1}{x^{6}}}$

Step 3.2

Combine $64$ and $\frac{1}{x^{6}}$ .

$\frac{\frac{256}{x^{8}}}{\frac{64}{x^{6}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{256}{x^{8}} \cdot \frac{x^{6}}{64}$

Step 5

Combine.

$\frac{256 x^{6}}{x^{8} \cdot 64}$

Step 6

Cancel the common factor of $256$ and $64$ .

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Step 6.1

Factor $64$ out of $256 x^{6}$ .

$\frac{64 (4 x^{6})}{x^{8} \cdot 64}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $64$ out of $x^{8} \cdot 64$ .

$\frac{64 (4 x^{6})}{64 \cdot x^{8}}$

Step 6.2.2

Cancel the common factor.

$\frac{64 (4 x^{6})}{64 \cdot x^{8}}$

Step 6.2.3

Rewrite the expression.

$\frac{4 x^{6}}{x^{8}}$

Step 7

Cancel the common factor of $x^{6}$ and $x^{8}$ .

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Step 7.1

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

$\frac{x^{6} \cdot 4}{x^{8}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x^{6}$ out of $x^{8}$ .

$\frac{x^{6} \cdot 4}{x^{6} x^{2}}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{6} \cdot 4}{x^{6} x^{2}}$

Step 7.2.3

Rewrite the expression.

$\frac{4}{x^{2}}$