Basic Math Examples

$8^{\frac{1}{3}} \cdot 25^{\frac{1}{2}}$

Step 1

Simplify the expression.

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Step 1.1

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{\frac{1}{3}} \cdot 25^{\frac{1}{2}}$

Step 1.2

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

$2^{3 (\frac{1}{3})} \cdot 25^{\frac{1}{2}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$2^{3 (\frac{1}{3})} \cdot 25^{\frac{1}{2}}$

Step 2.2

Rewrite the expression.

$2^{1} \cdot 25^{\frac{1}{2}}$

Step 3

Evaluate the exponent.

$2 \cdot 25^{\frac{1}{2}}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $25$ as $5^{2}$ .

$2 \cdot {(5^{2})}^{\frac{1}{2}}$

Step 4.2

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

$2 \cdot 5^{2 (\frac{1}{2})}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$2 \cdot 5^{2 (\frac{1}{2})}$

Step 5.2

Rewrite the expression.

$2 \cdot 5^{1}$

Step 6

Evaluate the exponent.

$2 \cdot 5$

Step 7

Multiply $2$ by $5$ .

$10$