Algebra Examples

$\frac{{(- 2 h k^{4})}^{3}}{2 h^{- 8} k^{- 8}}$

Step 1

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

$\frac{{(- 2 h k^{4})}^{3} h^{8}}{2 k^{- 8}}$

Step 2

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

$\frac{{(- 2 h k^{4})}^{3} h^{8} k^{8}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{{(- 2 h)}^{3} {(k^{4})}^{3} h^{8} k^{8}}{2}$

Step 3.2

Apply the product rule to $- 2 h$ .

$\frac{{(- 2)}^{3} h^{3} {(k^{4})}^{3} h^{8} k^{8}}{2}$

Step 3.3

Raise $- 2$ to the power of $3$ .

$\frac{- 8 h^{3} {(k^{4})}^{3} h^{8} k^{8}}{2}$

Step 3.4

Multiply the exponents in ${(k^{4})}^{3}$ .

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Step 3.4.1

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

$\frac{- 8 h^{3} k^{4 \cdot 3} h^{8} k^{8}}{2}$

Step 3.4.2

Multiply $4$ by $3$ .

$\frac{- 8 h^{3} k^{12} h^{8} k^{8}}{2}$

Step 3.5

Combine exponents.

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Step 3.5.1

Multiply $h^{3}$ by $h^{8}$ by adding the exponents.

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Step 3.5.1.1

Move $h^{8}$ .

$\frac{- 8 (h^{8} h^{3}) k^{12} k^{8}}{2}$

Step 3.5.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 8 h^{8 + 3} k^{12} k^{8}}{2}$

Step 3.5.1.3

Add $8$ and $3$ .

$\frac{- 8 h^{11} k^{12} k^{8}}{2}$

Step 3.5.2

Multiply $k^{12}$ by $k^{8}$ by adding the exponents.

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Step 3.5.2.1

Move $k^{8}$ .

$\frac{- 8 h^{11} (k^{8} k^{12})}{2}$

Step 3.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 8 h^{11} k^{8 + 12}}{2}$

Step 3.5.2.3

Add $8$ and $12$ .

$\frac{- 8 h^{11} k^{20}}{2}$

Step 4

Cancel the common factor of $- 8$ and $2$ .

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Step 4.1

Factor $2$ out of $- 8 h^{11} k^{20}$ .

$\frac{2 (- 4 h^{11} k^{20})}{2}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2$ .

$\frac{2 (- 4 h^{11} k^{20})}{2 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (- 4 h^{11} k^{20})}{2 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{- 4 h^{11} k^{20}}{1}$

Step 4.2.4

Divide $- 4 h^{11} k^{20}$ by $1$ .

$- 4 h^{11} k^{20}$