Basic Math Examples

$125^{\frac{2}{3}} + 81^{\frac{3}{4}}$

Step 1

Simplify each term.

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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 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

$5^{2} + 81^{\frac{3}{4}}$

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

Cancel the common factor of $4$ .

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Step 1.7.1

Cancel the common factor.

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

Step 1.7.2

Rewrite the expression.

$25 + 3^{3}$

Step 1.8

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

$25 + 27$

Step 2

Add $25$ and $27$ .

$52$