Algebra Examples

$\frac{{(2 p^{- 1})}^{5}}{6 j^{- 8} p^{- 8}}$

Step 1

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

$\frac{{(2 p^{- 1})}^{5} j^{8}}{6 p^{- 8}}$

Step 2

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

$\frac{{(2 p^{- 1})}^{5} j^{8} p^{8}}{6}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the product rule to $2 p^{- 1}$ .

$\frac{2^{5} {(p^{- 1})}^{5} j^{8} p^{8}}{6}$

Step 3.2

Raise $2$ to the power of $5$ .

$\frac{32 {(p^{- 1})}^{5} j^{8} p^{8}}{6}$

Step 3.3

Multiply the exponents in ${(p^{- 1})}^{5}$ .

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Step 3.3.1

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

$\frac{32 p^{- 1 \cdot 5} j^{8} p^{8}}{6}$

Step 3.3.2

Multiply $- 1$ by $5$ .

$\frac{32 p^{- 5} j^{8} p^{8}}{6}$

Step 3.4

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

$\frac{32 \frac{1}{p^{5}} j^{8} p^{8}}{6}$

Step 3.5

Combine exponents.

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Step 3.5.1

Combine $32$ and $\frac{1}{p^{5}}$ .

$\frac{\frac{32}{p^{5}} j^{8} p^{8}}{6}$

Step 3.5.2

Combine $\frac{32}{p^{5}}$ and $j^{8}$ .

$\frac{\frac{32 j^{8}}{p^{5}} p^{8}}{6}$

Step 3.5.3

Combine $\frac{32 j^{8}}{p^{5}}$ and $p^{8}$ .

$\frac{\frac{32 j^{8} p^{8}}{p^{5}}}{6}$

Step 3.6

Reduce the expression by cancelling the common factors.

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Step 3.6.1

Reduce the expression $\frac{32 j^{8} p^{8}}{p^{5}}$ by cancelling the common factors.

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Step 3.6.1.1

Factor $p^{5}$ out of $32 j^{8} p^{8}$ .

$\frac{\frac{p^{5} (32 j^{8} p^{3})}{p^{5}}}{6}$

Step 3.6.1.2

Multiply by $1$ .

$\frac{\frac{p^{5} (32 j^{8} p^{3})}{p^{5} \cdot 1}}{6}$

Step 3.6.1.3

Cancel the common factor.

$\frac{\frac{p^{5} (32 j^{8} p^{3})}{p^{5} \cdot 1}}{6}$

Step 3.6.1.4

Rewrite the expression.

$\frac{\frac{32 j^{8} p^{3}}{1}}{6}$

Step 3.6.2

Divide $32 j^{8} p^{3}$ by $1$ .

$\frac{32 j^{8} p^{3}}{6}$

Step 4

Cancel the common factor of $32$ and $6$ .

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Step 4.1

Factor $2$ out of $32 j^{8} p^{3}$ .

$\frac{2 (16 j^{8} p^{3})}{6}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $6$ .

$\frac{2 (16 j^{8} p^{3})}{2 (3)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (16 j^{8} p^{3})}{2 \cdot 3}$

Step 4.2.3

Rewrite the expression.

$\frac{16 j^{8} p^{3}}{3}$