Finite Math Examples

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

$8^{- \frac{1}{3}}$

Step 1

Set

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

$8^{- \frac{1}{3}}$ equal to

0

$0$ .

8^{- \frac{1}{3}} = 0

$8^{- \frac{1}{3}} = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Simplify

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

$8^{- \frac{1}{3}}$ .

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Step 2.1.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{8^{\frac{1}{3}}} = 0

$\frac{1}{8^{\frac{1}{3}}} = 0$

Step 2.1.2

Simplify the denominator.

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Step 2.1.2.1

Rewrite

8

$8$ as

2^{3}

$2^{3}$ .

\frac{1}{{(2^{3})}^{\frac{1}{3}}} = 0

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

Step 2.1.2.2

Apply the power rule and multiply exponents,

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

${(a^{m})}^{n} = a^{m n}$ .

\frac{1}{2^{3 (\frac{1}{3})}} = 0

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

Step 2.1.2.3

Cancel the common factor of

3

$3$ .

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Step 2.1.2.3.1

Cancel the common factor.

\frac{1}{2^{3 (\frac{1}{3})}} = 0

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

Step 2.1.2.3.2

Rewrite the expression.

\frac{1}{2^{1}} = 0

$\frac{1}{2^{1}} = 0$

\frac{1}{2^{1}} = 0

$\frac{1}{2^{1}} = 0$

Step 2.1.2.4

Evaluate the exponent.

\frac{1}{2} = 0

$\frac{1}{2} = 0$

\frac{1}{2} = 0

$\frac{1}{2} = 0$

\frac{1}{2} = 0

$\frac{1}{2} = 0$

Step 2.2

Since

\frac{1}{2} \neq 0

$\frac{1}{2} \neq 0$ , there are no solutions.

No solution

No solution

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$