Basic Math Examples

$\sqrt[4]{28} \div \sqrt[3]{7}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[4]{28}}{\sqrt[3]{7}}$

Step 2

Multiply $\frac{\sqrt[4]{28}}{\sqrt[3]{7}}$ by $\frac{{\sqrt[3]{7}}^{2}}{{\sqrt[3]{7}}^{2}}$ .

$\frac{\sqrt[4]{28}}{\sqrt[3]{7}} \cdot \frac{{\sqrt[3]{7}}^{2}}{{\sqrt[3]{7}}^{2}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{\sqrt[4]{28}}{\sqrt[3]{7}}$ by $\frac{{\sqrt[3]{7}}^{2}}{{\sqrt[3]{7}}^{2}}$ .

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{\sqrt[3]{7} {\sqrt[3]{7}}^{2}}$

Step 3.2

Raise $\sqrt[3]{7}$ to the power of $1$ .

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{{\sqrt[3]{7}}^{1} {\sqrt[3]{7}}^{2}}$

Step 3.3

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

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{{\sqrt[3]{7}}^{1 + 2}}$

Step 3.4

Add $1$ and $2$ .

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{{\sqrt[3]{7}}^{3}}$

Step 3.5

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

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Step 3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7}$ as $7^{\frac{1}{3}}$ .

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{{(7^{\frac{1}{3}})}^{3}}$

Step 3.5.2

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

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{7^{\frac{1}{3} \cdot 3}}$

Step 3.5.3

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

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{7^{\frac{3}{3}}}$

Step 3.5.4

Cancel the common factor of $3$ .

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Step 3.5.4.1

Cancel the common factor.

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{7^{\frac{3}{3}}}$

Step 3.5.4.2

Rewrite the expression.

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{7^{1}}$

Step 3.5.5

Evaluate the exponent.

$\frac{\sqrt[4]{28} {\sqrt[3]{7}}^{2}}{7}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite ${\sqrt[3]{7}}^{2}$ as $\sqrt[3]{7^{2}}$ .

$\frac{\sqrt[4]{28} \sqrt[3]{7^{2}}}{7}$

Step 4.2

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

$\frac{\sqrt[4]{28} \sqrt[3]{49}}{7}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite the expression using the least common index of $12$ .

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Step 5.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{28}$ as $28^{\frac{1}{4}}$ .

$\frac{28^{\frac{1}{4}} \sqrt[3]{49}}{7}$

Step 5.1.2

Rewrite $28^{\frac{1}{4}}$ as $28^{\frac{3}{12}}$ .

$\frac{28^{\frac{3}{12}} \sqrt[3]{49}}{7}$

Step 5.1.3

Rewrite $28^{\frac{3}{12}}$ as $\sqrt[12]{28^{3}}$ .

$\frac{\sqrt[12]{28^{3}} \sqrt[3]{49}}{7}$

Step 5.1.4

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

$\frac{\sqrt[12]{28^{3}} \cdot 49^{\frac{1}{3}}}{7}$

Step 5.1.5

Rewrite $49^{\frac{1}{3}}$ as $49^{\frac{4}{12}}$ .

$\frac{\sqrt[12]{28^{3}} \cdot 49^{\frac{4}{12}}}{7}$

Step 5.1.6

Rewrite $49^{\frac{4}{12}}$ as $\sqrt[12]{49^{4}}$ .

$\frac{\sqrt[12]{28^{3}} \sqrt[12]{49^{4}}}{7}$

Step 5.2

Combine using the product rule for radicals.

$\frac{\sqrt[12]{28^{3} \cdot 49^{4}}}{7}$

Step 5.3

Raise $28$ to the power of $3$ .

$\frac{\sqrt[12]{21952 \cdot 49^{4}}}{7}$

Step 5.4

Raise $49$ to the power of $4$ .

$\frac{\sqrt[12]{21952 \cdot 5764801}}{7}$

Step 6

Multiply $21952$ by $5764801$ .

$\frac{\sqrt[12]{126548911552}}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[12]{126548911552}}{7}$

Decimal Form:

$1.20251405 \dots$