Algebra Examples

$\sqrt[3]{\frac{64}{49}}$

Step 1

Rewrite $\sqrt[3]{\frac{64}{49}}$ as $\frac{\sqrt[3]{64}}{\sqrt[3]{49}}$ .

$\frac{\sqrt[3]{64}}{\sqrt[3]{49}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $64$ as $4^{3}$ .

$\frac{\sqrt[3]{4^{3}}}{\sqrt[3]{49}}$

Step 2.2

Pull terms out from under the radical.

$\frac{4}{\sqrt[3]{49}}$

Step 3

Multiply $\frac{4}{\sqrt[3]{49}}$ by $\frac{{\sqrt[3]{49}}^{2}}{{\sqrt[3]{49}}^{2}}$ .

$\frac{4}{\sqrt[3]{49}} \cdot \frac{{\sqrt[3]{49}}^{2}}{{\sqrt[3]{49}}^{2}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{4}{\sqrt[3]{49}}$ by $\frac{{\sqrt[3]{49}}^{2}}{{\sqrt[3]{49}}^{2}}$ .

$\frac{4 {\sqrt[3]{49}}^{2}}{\sqrt[3]{49} {\sqrt[3]{49}}^{2}}$

Step 4.2

Raise $\sqrt[3]{49}$ to the power of $1$ .

$\frac{4 {\sqrt[3]{49}}^{2}}{{\sqrt[3]{49}}^{1} {\sqrt[3]{49}}^{2}}$

Step 4.3

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

$\frac{4 {\sqrt[3]{49}}^{2}}{{\sqrt[3]{49}}^{1 + 2}}$

Step 4.4

Add $1$ and $2$ .

$\frac{4 {\sqrt[3]{49}}^{2}}{{\sqrt[3]{49}}^{3}}$

Step 4.5

Rewrite ${\sqrt[3]{49}}^{3}$ as $49$ .

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Step 4.5.1

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

$\frac{4 {\sqrt[3]{49}}^{2}}{{(49^{\frac{1}{3}})}^{3}}$

Step 4.5.2

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

$\frac{4 {\sqrt[3]{49}}^{2}}{49^{\frac{1}{3} \cdot 3}}$

Step 4.5.3

Combine $\frac{1}{3}$ and $3$ .

$\frac{4 {\sqrt[3]{49}}^{2}}{49^{\frac{3}{3}}}$

Step 4.5.4

Cancel the common factor of $3$ .

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Step 4.5.4.1

Cancel the common factor.

$\frac{4 {\sqrt[3]{49}}^{2}}{49^{\frac{3}{3}}}$

Step 4.5.4.2

Rewrite the expression.

$\frac{4 {\sqrt[3]{49}}^{2}}{49^{1}}$

Step 4.5.5

Evaluate the exponent.

$\frac{4 {\sqrt[3]{49}}^{2}}{49}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite ${\sqrt[3]{49}}^{2}$ as $\sqrt[3]{49^{2}}$ .

$\frac{4 \sqrt[3]{49^{2}}}{49}$

Step 5.2

Raise $49$ to the power of $2$ .

$\frac{4 \sqrt[3]{2401}}{49}$

Step 5.3

Rewrite $2401$ as $7^{3} \cdot 7$ .

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Step 5.3.1

Factor $343$ out of $2401$ .

$\frac{4 \sqrt[3]{343 (7)}}{49}$

Step 5.3.2

Rewrite $343$ as $7^{3}$ .

$\frac{4 \sqrt[3]{7^{3} \cdot 7}}{49}$

Step 5.4

Pull terms out from under the radical.

$\frac{4 \cdot 7 \sqrt[3]{7}}{49}$

Step 5.5

Multiply $4$ by $7$ .

$\frac{28 \sqrt[3]{7}}{49}$

Step 6

Cancel the common factor of $28$ and $49$ .

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Step 6.1

Factor $7$ out of $28 \sqrt[3]{7}$ .

$\frac{7 (4 \sqrt[3]{7})}{49}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $49$ .

$\frac{7 (4 \sqrt[3]{7})}{7 (7)}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (4 \sqrt[3]{7})}{7 \cdot 7}$

Step 6.2.3

Rewrite the expression.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.09310353 \dots$