Algebra Examples

$(25^{\frac{1}{2}}) (64^{\frac{1}{3}})$

Step 1

Simplify the expression.

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Step 1.1

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

${(5^{2})}^{\frac{1}{2}} \cdot 64^{\frac{1}{3}}$

Step 1.2

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

$5^{2 (\frac{1}{2})} \cdot 64^{\frac{1}{3}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$5^{2 (\frac{1}{2})} \cdot 64^{\frac{1}{3}}$

Step 2.2

Rewrite the expression.

$5^{1} \cdot 64^{\frac{1}{3}}$

Step 3

Evaluate the exponent.

$5 \cdot 64^{\frac{1}{3}}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $64$ as $4^{3}$ .

$5 \cdot {(4^{3})}^{\frac{1}{3}}$

Step 4.2

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

$5 \cdot 4^{3 (\frac{1}{3})}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

$5 \cdot 4^{3 (\frac{1}{3})}$

Step 5.2

Rewrite the expression.

$5 \cdot 4^{1}$

Step 6

Simplify the expression.

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Step 6.1

Evaluate the exponent.

$5 \cdot 4$

Step 6.2

Multiply $5$ by $4$ .

$20$