Simplify the Radical Expression 3/( fourth root of 4a^4)

$\frac{3}{\sqrt[4]{4 a^{4}}}$

Step 1

Simplify the denominator.

Reorder $4$ and $a^{4}$ .

$\frac{3}{\sqrt[4]{a^{4} \cdot 4}}$

Pull terms out from under the radical.

$\frac{3}{| a | \sqrt[4]{4}}$

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

$\frac{3}{| a | \sqrt[4]{2^{2}}}$

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$\frac{3}{| a | \sqrt{\sqrt{2^{2}}}}$

Pull terms out from under the radical.

$\frac{3}{| a | \sqrt{| 2 |}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{3}{| a | \sqrt{2}}$

Step 2

Multiply $\frac{3}{| a | \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{3}{| a | \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{3}{| a | \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{3 \sqrt{2}}{| a | \sqrt{2} \sqrt{2}}$

Move $\sqrt{2}$ .

$\frac{3 \sqrt{2}}{| a | (\sqrt{2} \sqrt{2})}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 \sqrt{2}}{| a | ({\sqrt{2}}^{1} \sqrt{2})}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 \sqrt{2}}{| a | ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \sqrt{2}}{| a | {\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 \sqrt{2}}{| a | {\sqrt{2}}^{2}}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{3 \sqrt{2}}{| a | {(2^{\frac{1}{2}})}^{2}}$

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

$\frac{3 \sqrt{2}}{| a | \cdot 2^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{3 \sqrt{2}}{| a | \cdot 2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \sqrt{2}}{| a | \cdot 2^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{3 \sqrt{2}}{| a | \cdot 2^{1}}$

Evaluate the exponent.

$\frac{3 \sqrt{2}}{| a | \cdot 2}$

Step 4

Move $2$ to the left of $| a |$ .

$\frac{3 \sqrt{2}}{2 | a |}$

Simplify the Radical Expression 3/( fourth root of 4a^4)

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