Basic Math Examples

${(125)}^{\frac{2}{3}} {(81)}^{- \frac{3}{4}}$

Step 1

Simplify the expression.

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Step 1.1

Rewrite $125$ as $5^{3}$ .

${(5^{3})}^{\frac{2}{3}} {(81)}^{- \frac{3}{4}}$

Step 1.2

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

$5^{3 (\frac{2}{3})} {(81)}^{- \frac{3}{4}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$5^{3 (\frac{2}{3})} {(81)}^{- \frac{3}{4}}$

Step 2.2

Rewrite the expression.

$5^{2} {(81)}^{- \frac{3}{4}}$

Step 3

Raise $5$ to the power of $2$ .

$25 {(81)}^{- \frac{3}{4}}$

Step 4

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

$25 \frac{1}{81^{\frac{3}{4}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $81$ as $3^{4}$ .

$25 \frac{1}{{(3^{4})}^{\frac{3}{4}}}$

Step 5.2

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

$25 \frac{1}{3^{4 (\frac{3}{4})}}$

Step 5.3

Cancel the common factor of $4$ .

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Step 5.3.1

Cancel the common factor.

$25 \frac{1}{3^{4 (\frac{3}{4})}}$

Step 5.3.2

Rewrite the expression.

$25 \frac{1}{3^{3}}$

Step 5.4

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

$25 (\frac{1}{27})$

Step 6

Combine $25$ and $\frac{1}{27}$ .

$\frac{25}{27}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{27}$

Decimal Form:

$0.\overline{925}$