Basic Math Examples

- {(\frac{1}{125})}^{- \frac{4}{3}}

$- {(\frac{1}{125})}^{- \frac{4}{3}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

- 125^{\frac{4}{3}}

$- 125^{\frac{4}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite

125

$125$ as

5^{3}

$5^{3}$ .

- {(5^{3})}^{\frac{4}{3}}

$- {(5^{3})}^{\frac{4}{3}}$

Step 2.2

Apply the power rule and multiply exponents,

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

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

- 5^{3 (\frac{4}{3})}

$- 5^{3 (\frac{4}{3})}$

- 5^{3 (\frac{4}{3})}

$- 5^{3 (\frac{4}{3})}$

Step 3

Cancel the common factor of

3

$3$ .

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Step 3.1

Cancel the common factor.

$- 5^{3 (\frac{4}{3})}$

Step 3.2

Rewrite the expression.

$- 5^{4}$

Step 4

Simplify the expression.

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Step 4.1

Raise

$5$ to the power of

$4$ .

$- 1 \cdot 625$

Step 4.2

Multiply

$- 1$ by

$625$ .

$- 625$