Basic Math Examples

$g (- 3) = {(\frac{1}{7})}^{- 3}$

Step 1

Divide each term in $g (- 3) = {(\frac{1}{7})}^{- 3}$ by $- 3$ .

$\frac{g \cdot - 3}{- 3} = \frac{{(\frac{1}{7})}^{- 3}}{- 3}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $- 3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{g \cdot - 3}{- 3} = \frac{{(\frac{1}{7})}^{- 3}}{- 3}$

Step 2.1.2

Divide $g$ by $1$ .

$g = \frac{{(\frac{1}{7})}^{- 3}}{- 3}$

Step 3

Simplify the right side.

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Step 3.1

Move ${(\frac{1}{7})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$g = \frac{1}{- 3 {(\frac{1}{7})}^{3}}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Apply the product rule to $\frac{1}{7}$ .

$g = \frac{1}{- 3 \frac{1^{3}}{7^{3}}}$

Step 3.2.2

One to any power is one.

$g = \frac{1}{- 3 \frac{1}{7^{3}}}$

Step 3.2.3

Raise $7$ to the power of $3$ .

$g = \frac{1}{- 3 (\frac{1}{343})}$

Step 3.3

Simplify terms.

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Step 3.3.1

Combine $- 3$ and $\frac{1}{343}$ .

$g = \frac{1}{\frac{- 3}{343}}$

Step 3.3.2

Move the negative in front of the fraction.

$g = \frac{1}{- \frac{3}{343}}$

Step 3.3.3

Cancel the common factor of $1$ and $- 1$ .

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Step 3.3.3.1

Rewrite $1$ as $- 1 (- 1)$ .

$g = \frac{- 1 (- 1)}{- \frac{3}{343}}$

Step 3.3.3.2

Move the negative in front of the fraction.

$g = - \frac{1}{\frac{3}{343}}$

Step 3.4

Multiply the numerator by the reciprocal of the denominator.

$g = - (1 (\frac{343}{3}))$

Step 3.5

Multiply $\frac{343}{3}$ by $1$ .

$g = - \frac{343}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$g = - \frac{343}{3}$

Decimal Form:

$g = - 114.\overline{3}$

Mixed Number Form:

$g = - 114 \frac{1}{3}$