Algebra Examples

$\frac{\sqrt[3]{7^{2}}}{\sqrt{7}}$

Step 1

Raise $7$ to the power of $2$ .

$\frac{\sqrt[3]{49}}{\sqrt{7}}$

Step 2

Multiply $\frac{\sqrt[3]{49}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt[3]{49}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{\sqrt[3]{49}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt[3]{49} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Step 3.2

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

$\frac{\sqrt[3]{49} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 3.3

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

$\frac{\sqrt[3]{49} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

Step 3.4

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

$\frac{\sqrt[3]{49} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{\sqrt[3]{49} \sqrt{7}}{{\sqrt{7}}^{2}}$

Step 3.6

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

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Step 3.6.1

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

$\frac{\sqrt[3]{49} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

Step 3.6.2

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

$\frac{\sqrt[3]{49} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

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

$\frac{\sqrt[3]{49} \sqrt{7}}{7^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{\sqrt[3]{49} \sqrt{7}}{7^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{\sqrt[3]{49} \sqrt{7}}{7^{1}}$

Step 3.6.5

Evaluate the exponent.

$\frac{\sqrt[3]{49} \sqrt{7}}{7}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite the expression using the least common index of $6$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{49}$ as $49^{\frac{1}{3}}$ .

$\frac{49^{\frac{1}{3}} \sqrt{7}}{7}$

Step 4.1.2

Rewrite $49^{\frac{1}{3}}$ as $49^{\frac{2}{6}}$ .

$\frac{49^{\frac{2}{6}} \sqrt{7}}{7}$

Step 4.1.3

Rewrite $49^{\frac{2}{6}}$ as $\sqrt[6]{49^{2}}$ .

$\frac{\sqrt[6]{49^{2}} \sqrt{7}}{7}$

Step 4.1.4

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

$\frac{\sqrt[6]{49^{2}} \cdot 7^{\frac{1}{2}}}{7}$

Step 4.1.5

Rewrite $7^{\frac{1}{2}}$ as $7^{\frac{3}{6}}$ .

$\frac{\sqrt[6]{49^{2}} \cdot 7^{\frac{3}{6}}}{7}$

Step 4.1.6

Rewrite $7^{\frac{3}{6}}$ as $\sqrt[6]{7^{3}}$ .

$\frac{\sqrt[6]{49^{2}} \sqrt[6]{7^{3}}}{7}$

Step 4.2

Combine using the product rule for radicals.

$\frac{\sqrt[6]{49^{2} \cdot 7^{3}}}{7}$

Step 4.3

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt[6]{{(7^{2})}^{2} \cdot 7^{3}}}{7}$

Step 4.4

Multiply the exponents in ${(7^{2})}^{2}$ .

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Step 4.4.1

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

$\frac{\sqrt[6]{7^{2 \cdot 2} \cdot 7^{3}}}{7}$

Step 4.4.2

Multiply $2$ by $2$ .

$\frac{\sqrt[6]{7^{4} \cdot 7^{3}}}{7}$

Step 4.5

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

$\frac{\sqrt[6]{7^{4 + 3}}}{7}$

Step 4.6

Add $4$ and $3$ .

$\frac{\sqrt[6]{7^{7}}}{7}$

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{\sqrt[6]{823543}}{7}$

Step 5.2

Rewrite $823543$ as $7^{6} \cdot 7$ .

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Step 5.2.1

Factor $117649$ out of $823543$ .

$\frac{\sqrt[6]{117649 (7)}}{7}$

Step 5.2.2

Rewrite $117649$ as $7^{6}$ .

$\frac{\sqrt[6]{7^{6} \cdot 7}}{7}$

Step 5.3

Pull terms out from under the radical.

$\frac{7 \sqrt[6]{7}}{7}$

Step 6

Cancel the common factor of $7$ .

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Step 6.1

Cancel the common factor.

$\frac{7 \sqrt[6]{7}}{7}$

Step 6.2

Divide $\sqrt[6]{7}$ by $1$ .

$\sqrt[6]{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{7}$

Decimal Form:

$1.38308755 \dots$