Basic Math Examples

{(- \frac{1}{3})}^{3}

${(- \frac{1}{3})}^{3}$

Step 1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 1.1

Apply the product rule to

- \frac{1}{3}

$- \frac{1}{3}$ .

{(- 1)}^{3} {(\frac{1}{3})}^{3}

${(- 1)}^{3} {(\frac{1}{3})}^{3}$

Step 1.2

Apply the product rule to

\frac{1}{3}

$\frac{1}{3}$ .

{(- 1)}^{3} \frac{1^{3}}{3^{3}}

${(- 1)}^{3} \frac{1^{3}}{3^{3}}$

{(- 1)}^{3} \frac{1^{3}}{3^{3}}

${(- 1)}^{3} \frac{1^{3}}{3^{3}}$

Step 2

Raise

- 1

$- 1$ to the power of

3

$3$ .

- \frac{1^{3}}{3^{3}}

$- \frac{1^{3}}{3^{3}}$

Step 3

One to any power is one.

- \frac{1}{3^{3}}

$- \frac{1}{3^{3}}$

Step 4

Raise

3

$3$ to the power of

3

$3$ .

- \frac{1}{27}

$- \frac{1}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

- \frac{1}{27}

$- \frac{1}{27}$

Decimal Form:

- 0. ¯ ¯¯¯¯ ¯ 037

$- 0.\overline{037}$