Trigonometry Examples

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

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 $4 a^{2} b^{4}$ .

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

Step 1.2

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

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Evaluate the exponent.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Rewrite the expression.

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

Step 6

Simplify.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factor of $2$ .

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Step 7.2.1

Factor $2$ out of $4$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$2 a b^{2}$