Basic Math Examples

$81 \sqrt[3]{\frac{375}{729}}$

Step 1

Cancel the common factor of $375$ and $729$ .

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Step 1.1

Factor $3$ out of $375$ .

$81 \sqrt[3]{\frac{3 (125)}{729}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $729$ .

$81 \sqrt[3]{\frac{3 \cdot 125}{3 \cdot 243}}$

Step 1.2.2

Cancel the common factor.

$81 \sqrt[3]{\frac{3 \cdot 125}{3 \cdot 243}}$

Step 1.2.3

Rewrite the expression.

$81 \sqrt[3]{\frac{125}{243}}$

Step 2

Rewrite $\sqrt[3]{\frac{125}{243}}$ as $\frac{\sqrt[3]{125}}{\sqrt[3]{243}}$ .

$81 \frac{\sqrt[3]{125}}{\sqrt[3]{243}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $125$ as $5^{3}$ .

$81 \frac{\sqrt[3]{5^{3}}}{\sqrt[3]{243}}$

Step 3.2

Pull terms out from under the radical, assuming real numbers.

$81 \frac{5}{\sqrt[3]{243}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $243$ as $3^{3} \cdot 9$ .

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Step 4.1.1

Factor $27$ out of $243$ .

$81 \frac{5}{\sqrt[3]{27 (9)}}$

Step 4.1.2

Rewrite $27$ as $3^{3}$ .

$81 \frac{5}{\sqrt[3]{3^{3} \cdot 9}}$

Step 4.2

Pull terms out from under the radical.

$81 \frac{5}{3 \sqrt[3]{9}}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Factor $3$ out of $81$ .

$3 (27) \frac{5}{3 \sqrt[3]{9}}$

Step 5.1.2

Factor $3$ out of $3 \sqrt[3]{9}$ .

$3 (27) \frac{5}{3 (\sqrt[3]{9})}$

Step 5.1.3

Cancel the common factor.

$3 \cdot 27 \frac{5}{3 \sqrt[3]{9}}$

Step 5.1.4

Rewrite the expression.

$27 \frac{5}{\sqrt[3]{9}}$

Step 5.2

Combine $27$ and $\frac{5}{\sqrt[3]{9}}$ .

$\frac{27 \cdot 5}{\sqrt[3]{9}}$

Step 5.3

Multiply $27$ by $5$ .

$\frac{135}{\sqrt[3]{9}}$

Step 6

Multiply $\frac{135}{\sqrt[3]{9}}$ by $\frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$ .

$\frac{135}{\sqrt[3]{9}} \cdot \frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{135}{\sqrt[3]{9}}$ by $\frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$ .

$\frac{135 {\sqrt[3]{9}}^{2}}{\sqrt[3]{9} {\sqrt[3]{9}}^{2}}$

Step 7.2

Raise $\sqrt[3]{9}$ to the power of $1$ .

$\frac{135 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{1} {\sqrt[3]{9}}^{2}}$

Step 7.3

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

$\frac{135 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{1 + 2}}$

Step 7.4

Add $1$ and $2$ .

$\frac{135 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{3}}$

Step 7.5

Rewrite ${\sqrt[3]{9}}^{3}$ as $9$ .

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Step 7.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

$\frac{135 {\sqrt[3]{9}}^{2}}{{(9^{\frac{1}{3}})}^{3}}$

Step 7.5.2

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

$\frac{135 {\sqrt[3]{9}}^{2}}{9^{\frac{1}{3} \cdot 3}}$

Step 7.5.3

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

$\frac{135 {\sqrt[3]{9}}^{2}}{9^{\frac{3}{3}}}$

Step 7.5.4

Cancel the common factor of $3$ .

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Step 7.5.4.1

Cancel the common factor.

$\frac{135 {\sqrt[3]{9}}^{2}}{9^{\frac{3}{3}}}$

Step 7.5.4.2

Rewrite the expression.

$\frac{135 {\sqrt[3]{9}}^{2}}{9^{1}}$

Step 7.5.5

Evaluate the exponent.

$\frac{135 {\sqrt[3]{9}}^{2}}{9}$

Step 8

Cancel the common factor of $135$ and $9$ .

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Step 8.1

Factor $9$ out of $135 {\sqrt[3]{9}}^{2}$ .

$\frac{9 (15 {\sqrt[3]{9}}^{2})}{9}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $9$ out of $9$ .

$\frac{9 (15 {\sqrt[3]{9}}^{2})}{9 (1)}$

Step 8.2.2

Cancel the common factor.

$\frac{9 (15 {\sqrt[3]{9}}^{2})}{9 \cdot 1}$

Step 8.2.3

Rewrite the expression.

$\frac{15 {\sqrt[3]{9}}^{2}}{1}$

Step 8.2.4

Divide $15 {\sqrt[3]{9}}^{2}$ by $1$ .

$15 {\sqrt[3]{9}}^{2}$

Step 9

Rewrite ${\sqrt[3]{9}}^{2}$ as $\sqrt[3]{9^{2}}$ .

$15 \sqrt[3]{9^{2}}$

Step 10

Raise $9$ to the power of $2$ .

$15 \sqrt[3]{81}$

Step 11

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 11.1

Factor $27$ out of $81$ .

$15 \sqrt[3]{27 (3)}$

Step 11.2

Rewrite $27$ as $3^{3}$ .

$15 \sqrt[3]{3^{3} \cdot 3}$

Step 12

Pull terms out from under the radical.

$15 (3 \sqrt[3]{3})$

Step 13

Multiply $3$ by $15$ .

$45 \sqrt[3]{3}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$45 \sqrt[3]{3}$

Decimal Form:

$64.90123066 \dots$