Basic Math Examples

$\frac{7 \cdot \sqrt[3]{\frac{6}{5^{10}}}}{1}$

Step 1

Divide $7 \cdot \sqrt[3]{\frac{6}{5^{10}}}$ by $1$ .

$7 \cdot \sqrt[3]{\frac{6}{5^{10}}}$

Step 2

Raise $5$ to the power of $10$ .

$7 \cdot \sqrt[3]{\frac{6}{9765625}}$

Step 3

Rewrite $\sqrt[3]{\frac{6}{9765625}}$ as $\frac{\sqrt[3]{6}}{\sqrt[3]{9765625}}$ .

$7 \cdot \frac{\sqrt[3]{6}}{\sqrt[3]{9765625}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $9765625$ as $125^{3} \cdot 5$ .

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Step 4.1.1

Factor $1953125$ out of $9765625$ .

$7 \cdot \frac{\sqrt[3]{6}}{\sqrt[3]{1953125 (5)}}$

Step 4.1.2

Rewrite $1953125$ as $125^{3}$ .

$7 \cdot \frac{\sqrt[3]{6}}{\sqrt[3]{125^{3} \cdot 5}}$

Step 4.2

Pull terms out from under the radical.

$7 \cdot \frac{\sqrt[3]{6}}{125 \sqrt[3]{5}}$

Step 5

Multiply $\frac{\sqrt[3]{6}}{125 \sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$7 \cdot (\frac{\sqrt[3]{6}}{125 \sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{\sqrt[3]{6}}{125 \sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 \sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Step 6.2

Move $\sqrt[3]{5}$ .

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 (\sqrt[3]{5} {\sqrt[3]{5}}^{2})}$

Step 6.3

Raise $\sqrt[3]{5}$ to the power of $1$ .

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 ({\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2})}$

Step 6.4

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

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 {\sqrt[3]{5}}^{1 + 2}}$

Step 6.5

Add $1$ and $2$ .

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 {\sqrt[3]{5}}^{3}}$

Step 6.6

Rewrite ${\sqrt[3]{5}}^{3}$ as $5$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 {(5^{\frac{1}{3}})}^{3}}$

Step 6.6.2

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

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 \cdot 5^{\frac{1}{3} \cdot 3}}$

Step 6.6.3

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

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 \cdot 5^{\frac{3}{3}}}$

Step 6.6.4

Cancel the common factor of $3$ .

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Step 6.6.4.1

Cancel the common factor.

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 \cdot 5^{\frac{3}{3}}}$

Step 6.6.4.2

Rewrite the expression.

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 \cdot 5^{1}}$

Step 6.6.5

Evaluate the exponent.

$7 \cdot \frac{\sqrt[3]{6} {\sqrt[3]{5}}^{2}}{125 \cdot 5}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$7 \cdot \frac{\sqrt[3]{6} \sqrt[3]{5^{2}}}{125 \cdot 5}$

Step 7.2

Raise $5$ to the power of $2$ .

$7 \cdot \frac{\sqrt[3]{6} \sqrt[3]{25}}{125 \cdot 5}$

Step 8

Multiply $125$ by $5$ .

$7 \cdot \frac{\sqrt[3]{6} \sqrt[3]{25}}{625}$

Step 9

Simplify the numerator.

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Step 9.1

Combine using the product rule for radicals.

$7 \cdot \frac{\sqrt[3]{6 \cdot 25}}{625}$

Step 9.2

Multiply $6$ by $25$ .

$7 \cdot \frac{\sqrt[3]{150}}{625}$

Step 10

Combine $7$ and $\frac{\sqrt[3]{150}}{625}$ .

$\frac{7 \sqrt[3]{150}}{625}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{7 \sqrt[3]{150}}{625}$

Decimal Form:

$0.05950887 \dots$