Algebra Examples

$2 y^{- 9} h^{2} {(2 y^{0} h^{- 4})}^{- 6}$

Step 1

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

$2 \frac{1}{y^{9}} h^{2} {(2 y^{0} h^{- 4})}^{- 6}$

Step 2

Combine $2$ and $\frac{1}{y^{9}}$ .

$\frac{2}{y^{9}} h^{2} {(2 y^{0} h^{- 4})}^{- 6}$

Step 3

Combine $\frac{2}{y^{9}}$ and $h^{2}$ .

$\frac{2 h^{2}}{y^{9}} {(2 y^{0} h^{- 4})}^{- 6}$

Step 4

Simplify the expression.

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Step 4.1

Anything raised to $0$ is $1$ .

$\frac{2 h^{2}}{y^{9}} {(2 \cdot 1 h^{- 4})}^{- 6}$

Step 4.2

Multiply $2$ by $1$ .

$\frac{2 h^{2}}{y^{9}} {(2 h^{- 4})}^{- 6}$

Step 5

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

$\frac{2 h^{2}}{y^{9}} {(2 \frac{1}{h^{4}})}^{- 6}$

Step 6

Combine $2$ and $\frac{1}{h^{4}}$ .

$\frac{2 h^{2}}{y^{9}} {(\frac{2}{h^{4}})}^{- 6}$

Step 7

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{2 h^{2}}{y^{9}} {(\frac{h^{4}}{2})}^{6}$

Step 8

Apply the product rule to $\frac{h^{4}}{2}$ .

$\frac{2 h^{2}}{y^{9}} \cdot \frac{{(h^{4})}^{6}}{2^{6}}$

Step 9

Combine.

$\frac{2 h^{2} {(h^{4})}^{6}}{y^{9} \cdot 2^{6}}$

Step 10

Cancel the common factor of $2$ and $2^{6}$ .

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Step 10.1

Factor $2$ out of $2 h^{2} {(h^{4})}^{6}$ .

$\frac{2 (h^{2} {(h^{4})}^{6})}{y^{9} \cdot 2^{6}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $y^{9} \cdot 2^{6}$ .

$\frac{2 (h^{2} {(h^{4})}^{6})}{2 (y^{9} \cdot 2^{5})}$

Step 10.2.2

Cancel the common factor.

$\frac{2 (h^{2} {(h^{4})}^{6})}{2 (y^{9} \cdot 2^{5})}$

Step 10.2.3

Rewrite the expression.

$\frac{h^{2} {(h^{4})}^{6}}{y^{9} \cdot 2^{5}}$

Step 11

Simplify the expression.

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Step 11.1

Multiply the exponents in ${(h^{4})}^{6}$ .

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Step 11.1.1

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

$\frac{h^{2} h^{4 \cdot 6}}{y^{9} \cdot 2^{5}}$

Step 11.1.2

Multiply $4$ by $6$ .

$\frac{h^{2} h^{24}}{y^{9} \cdot 2^{5}}$

Step 11.2

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

$\frac{h^{2} h^{24}}{y^{9} \cdot 32}$

Step 12

Multiply $h^{2}$ by $h^{24}$ by adding the exponents.

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Step 12.1

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

$\frac{h^{2 + 24}}{y^{9} \cdot 32}$

Step 12.2

Add $2$ and $24$ .

$\frac{h^{26}}{y^{9} \cdot 32}$

Step 13

Move $32$ to the left of $y^{9}$ .

$\frac{h^{26}}{32 y^{9}}$