Algebra Examples

$\frac{{(2 g^{3} h^{- 2})}^{2}}{{(g^{2} h^{0})}^{- 3}}$

Step 1

Move ${(g^{2} h^{0})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(2 g^{3} h^{- 2})}^{2} {(g^{2} h^{0})}^{3}$

Step 2

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

${(2 g^{3} \frac{1}{h^{2}})}^{2} {(g^{2} h^{0})}^{3}$

Step 3

Multiply $2 g^{3} \frac{1}{h^{2}}$ .

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Step 3.1

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

${(g^{3} \frac{2}{h^{2}})}^{2} {(g^{2} h^{0})}^{3}$

Step 3.2

Combine $g^{3}$ and $\frac{2}{h^{2}}$ .

${(\frac{g^{3} \cdot 2}{h^{2}})}^{2} {(g^{2} h^{0})}^{3}$

Step 4

Move $2$ to the left of $g^{3}$ .

${(\frac{2 \cdot g^{3}}{h^{2}})}^{2} {(g^{2} h^{0})}^{3}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{2 g^{3}}{h^{2}}$ .

$\frac{{(2 g^{3})}^{2}}{{(h^{2})}^{2}} {(g^{2} h^{0})}^{3}$

Step 5.2

Apply the product rule to $2 g^{3}$ .

$\frac{2^{2} {(g^{3})}^{2}}{{(h^{2})}^{2}} {(g^{2} h^{0})}^{3}$

Step 6

Simplify the numerator.

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Step 6.1

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

$\frac{4 {(g^{3})}^{2}}{{(h^{2})}^{2}} {(g^{2} h^{0})}^{3}$

Step 6.2

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

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Step 6.2.1

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

$\frac{4 g^{3 \cdot 2}}{{(h^{2})}^{2}} {(g^{2} h^{0})}^{3}$

Step 6.2.2

Multiply $3$ by $2$ .

$\frac{4 g^{6}}{{(h^{2})}^{2}} {(g^{2} h^{0})}^{3}$

Step 7

Simplify the expression.

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Step 7.1

Multiply the exponents in ${(h^{2})}^{2}$ .

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Step 7.1.1

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

$\frac{4 g^{6}}{h^{2 \cdot 2}} {(g^{2} h^{0})}^{3}$

Step 7.1.2

Multiply $2$ by $2$ .

$\frac{4 g^{6}}{h^{4}} {(g^{2} h^{0})}^{3}$

Step 7.2

Anything raised to $0$ is $1$ .

$\frac{4 g^{6}}{h^{4}} {(g^{2} \cdot 1)}^{3}$

Step 7.3

Multiply $g^{2}$ by $1$ .

$\frac{4 g^{6}}{h^{4}} {(g^{2})}^{3}$

Step 7.4

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

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Step 7.4.1

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

$\frac{4 g^{6}}{h^{4}} g^{2 \cdot 3}$

Step 7.4.2

Multiply $2$ by $3$ .

$\frac{4 g^{6}}{h^{4}} g^{6}$

Step 8

Multiply $\frac{4 g^{6}}{h^{4}} g^{6}$ .

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Step 8.1

Combine $\frac{4 g^{6}}{h^{4}}$ and $g^{6}$ .

$\frac{4 g^{6} g^{6}}{h^{4}}$

Step 8.2

Multiply $g^{6}$ by $g^{6}$ by adding the exponents.

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Step 8.2.1

Move $g^{6}$ .

$\frac{4 (g^{6} g^{6})}{h^{4}}$

Step 8.2.2

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

$\frac{4 g^{6 + 6}}{h^{4}}$

Step 8.2.3

Add $6$ and $6$ .

$\frac{4 g^{12}}{h^{4}}$