Pre-Algebra Examples

$\frac{72 g^{9} g^{- 7}}{{(12 (- 1) (g^{- 3}))}^{4}}$

Step 1

Multiply $g^{9}$ by $g^{- 7}$ by adding the exponents.

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Step 1.1

Move $g^{- 7}$ .

$\frac{72 (g^{- 7} g^{9})}{{(12 (- 1) (g^{- 3}))}^{4}}$

Step 1.2

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

$\frac{72 g^{- 7 + 9}}{{(12 (- 1) (g^{- 3}))}^{4}}$

Step 1.3

Add $- 7$ and $9$ .

$\frac{72 g^{2}}{{(12 (- 1) (g^{- 3}))}^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Combine exponents.

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Step 2.1.1

Factor out negative.

$\frac{72 g^{2}}{{(- (12 g^{- 3}))}^{4}}$

Step 2.1.2

Multiply $12$ by $- 1$ .

$\frac{72 g^{2}}{{(- 12 g^{- 3})}^{4}}$

Step 2.2

Apply the product rule to $- 12 g^{- 3}$ .

$\frac{72 g^{2}}{{(- 12)}^{4} {(g^{- 3})}^{4}}$

Step 2.3

Raise $- 12$ to the power of $4$ .

$\frac{72 g^{2}}{20736 {(g^{- 3})}^{4}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{72 g^{2}}{20736 g^{- 3 \cdot 4}}$

Step 2.4.2

Multiply $- 3$ by $4$ .

$\frac{72 g^{2}}{20736 g^{- 12}}$

Step 2.5

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

$\frac{72 g^{2}}{20736 \frac{1}{g^{12}}}$

Step 3

Combine $20736$ and $\frac{1}{g^{12}}$ .

$\frac{72 g^{2}}{\frac{20736}{g^{12}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$72 g^{2} \frac{g^{12}}{20736}$

Step 5

Cancel the common factor of $72$ .

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Step 5.1

Factor $72$ out of $72 g^{2}$ .

$72 (g^{2}) \frac{g^{12}}{20736}$

Step 5.2

Factor $72$ out of $20736$ .

$72 (g^{2}) \frac{g^{12}}{72 (288)}$

Step 5.3

Cancel the common factor.

$72 g^{2} \frac{g^{12}}{72 \cdot 288}$

Step 5.4

Rewrite the expression.

$g^{2} \frac{g^{12}}{288}$

Step 6

Combine $g^{2}$ and $\frac{g^{12}}{288}$ .

$\frac{g^{2} g^{12}}{288}$

Step 7

Multiply $g^{2}$ by $g^{12}$ by adding the exponents.

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Step 7.1

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

$\frac{g^{2 + 12}}{288}$

Step 7.2

Add $2$ and $12$ .

$\frac{g^{14}}{288}$