Write the Fraction in Simplest Form ( fourth root of 9)/( fourth root of 4)

$\frac{\sqrt[4]{9}}{\sqrt[4]{4}}$

Step 1

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

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

Rewrite $\sqrt[4]{3^{2}}$ as $\sqrt{\sqrt{3^{2}}}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2

Simplify the denominator.

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

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

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

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

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

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

$\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

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

$\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt{3} \sqrt{2}}{2^{1}}$

Evaluate the exponent.

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

Step 5

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$\frac{\sqrt{6}}{2}$

Write the Fraction in Simplest Form ( fourth root of 9)/( fourth root of 4)

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