Simplify ( fourth root of 7)/( square root of 7)

$\frac{\sqrt[4]{7}}{\sqrt[2]{7}}$

Multiply $\frac{\sqrt[4]{7}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt[4]{7}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[4]{7}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt[4]{7} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt[4]{7} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt[4]{7} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

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

$\frac{\sqrt[4]{7} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt[4]{7} \sqrt{7}}{{\sqrt{7}}^{2}}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{7} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt[4]{7} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt[4]{7} \sqrt{7}}{7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt[4]{7} \sqrt{7}}{7^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt[4]{7} \sqrt{7}}{7^{1}}$

Evaluate the exponent.

$\frac{\sqrt[4]{7} \sqrt{7}}{7}$

Simplify the numerator.

Rewrite the expression using the least common index of $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{7} \cdot 7^{\frac{1}{2}}}{7}$

Rewrite $7^{\frac{1}{2}}$ as $7^{\frac{2}{4}}$ .

$\frac{\sqrt[4]{7} \cdot 7^{\frac{2}{4}}}{7}$

Rewrite $7^{\frac{2}{4}}$ as $\sqrt[4]{7^{2}}$ .

$\frac{\sqrt[4]{7} \sqrt[4]{7^{2}}}{7}$

Combine using the product rule for radicals.

$\frac{\sqrt[4]{7 \cdot 7^{2}}}{7}$

Multiply $7$ by $7^{2}$ by adding the exponents.

Multiply $7$ by $7^{2}$ .

Raise $7$ to the power of $1$ .

$\frac{\sqrt[4]{7^{1} \cdot 7^{2}}}{7}$

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

$\frac{\sqrt[4]{7^{1 + 2}}}{7}$

Add $1$ and $2$ .

$\frac{\sqrt[4]{7^{3}}}{7}$

Raise $7$ to the power of $3$ .

$\frac{\sqrt[4]{343}}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[4]{343}}{7}$

Decimal Form:

$0.61478815 \dots$

Simplify ( fourth root of 7)/( square root of 7)

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