Algebra Examples

${(16 a^{2} b^{4})}^{\frac{1}{4}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $16 a^{2} b^{4}$ .

${(16 a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 1.2

Apply the product rule to $16 a^{2}$ .

$16^{\frac{1}{4}} {(a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $16$ as $2^{4}$ .

${(2^{4})}^{\frac{1}{4}} {(a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 2.2

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

$2^{4 (\frac{1}{4})} {(a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$2^{4 (\frac{1}{4})} {(a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 3.2

Rewrite the expression.

$2^{1} {(a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 4

Evaluate the exponent.

$2 {(a^{2})}^{\frac{1}{4}} {(b^{4})}^{\frac{1}{4}}$

Step 5

Multiply the exponents in ${(a^{2})}^{\frac{1}{4}}$ .

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Step 5.1

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

$2 a^{2 (\frac{1}{4})} {(b^{4})}^{\frac{1}{4}}$

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Factor $2$ out of $4$ .

$2 a^{2 \frac{1}{2 (2)}} {(b^{4})}^{\frac{1}{4}}$

Step 5.2.2

Cancel the common factor.

$2 a^{2 \frac{1}{2 \cdot 2}} {(b^{4})}^{\frac{1}{4}}$

Step 5.2.3

Rewrite the expression.

$2 a^{\frac{1}{2}} {(b^{4})}^{\frac{1}{4}}$

Step 6

Multiply the exponents in ${(b^{4})}^{\frac{1}{4}}$ .

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Step 6.1

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

$2 a^{\frac{1}{2}} b^{4 (\frac{1}{4})}$

Step 6.2

Cancel the common factor of $4$ .

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Step 6.2.1

Cancel the common factor.

$2 a^{\frac{1}{2}} b^{4 (\frac{1}{4})}$

Step 6.2.2

Rewrite the expression.

$2 a^{\frac{1}{2}} b^{1}$

Step 7

Simplify.

$2 a^{\frac{1}{2}} b$

Step 8

Reorder factors in $2 a^{\frac{1}{2}} b$ .

$2 b a^{\frac{1}{2}}$