Algebra Examples

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

Step 1

Move $p^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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Step 2.1

Factor $4$ out of $4$ .

$\frac{4 (1)}{- 4 {(p^{- 2})}^{4} p^{8}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $- 4 {(p^{- 2})}^{4} p^{8}$ .

$\frac{4 (1)}{4 (- {(p^{- 2})}^{4} p^{8})}$

Step 2.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 (- {(p^{- 2})}^{4} p^{8})}$

Step 2.2.3

Rewrite the expression.

$\frac{1}{- {(p^{- 2})}^{4} p^{8}}$

Step 3

Cancel the common factor of $1$ and $- 1$ .

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Step 3.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- {(p^{- 2})}^{4} p^{8}}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{1}{{(p^{- 2})}^{4} p^{8}}$

Step 4

Simplify the denominator.

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Step 4.1

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

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Step 4.1.1

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

$- \frac{1}{p^{- 2 \cdot 4} p^{8}}$

Step 4.1.2

Multiply $- 2$ by $4$ .

$- \frac{1}{p^{- 8} p^{8}}$

Step 4.2

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

$- \frac{1}{\frac{1}{p^{8}} p^{8}}$

Step 5

Combine $\frac{1}{p^{8}}$ and $p^{8}$ .

$- \frac{1}{\frac{p^{8}}{p^{8}}}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Reduce the expression $\frac{p^{8}}{p^{8}}$ by cancelling the common factors.

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Step 6.1.1

Cancel the common factor.

$- \frac{1}{\frac{p^{8}}{p^{8}}}$

Step 6.1.2

Rewrite the expression.

$- \frac{1}{\frac{1}{1}}$

Step 6.2

Rewrite the expression.

$- \frac{1}{1}$

Step 7

Cancel the common factor of $1$ .

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Step 7.1

Cancel the common factor.

$- \frac{1}{1}$

Step 7.2

Rewrite the expression.

$- 1 \cdot 1$

Step 8

Multiply $- 1$ by $1$ .

$- 1$