Basic Math Examples

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

Step 1

Cancel the common factor of

$\sqrt[3]{4}$ .

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

Multiply

$\frac{\sqrt[3]{49}}{\sqrt[3]{2}}$ by

$1$ .

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

Step 3

Multiply

$\frac{\sqrt[3]{49}}{\sqrt[3]{2}}$ by

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

$\frac{\sqrt[3]{49}}{\sqrt[3]{2}}$ by

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

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

Step 4.2

Raise

$\sqrt[3]{2}$ to the power of

$1$ .

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

Step 4.3

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.4

Add

$1$ and

$2$ .

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

Step 4.5

Rewrite

${\sqrt[3]{2}}^{3}$ as

$2$ .

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Step 4.5.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt[3]{2}$ as

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

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

Step 4.5.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.5.3

Combine

$\frac{1}{3}$ and

$3$ .

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

Step 4.5.4

Cancel the common factor of

$3$ .

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Step 4.5.4.1

Cancel the common factor.

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

Step 4.5.4.2

Rewrite the expression.

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

Step 4.5.5

Evaluate the exponent.

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

Step 5

Simplify the numerator.

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Step 5.1

Rewrite

${\sqrt[3]{2}}^{2}$ as

$\sqrt[3]{2^{2}}$ .

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

Step 5.2

Raise

$2$ to the power of

$2$ .

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

Step 6

Simplify the numerator.

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Step 6.1

Combine using the product rule for radicals.

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

Step 6.2

Multiply

$49$ by

$4$ .

$\frac{\sqrt[3]{196}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[3]{196}}{2}$

Decimal Form:

$2.90439286 \dots$