Basic Math Examples

$\frac{{(\sqrt{729})}^{3}}{{(\sqrt{3375})}^{3}} \cdot 1325$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $729$ as $27^{2}$ .

$\frac{{\sqrt{27^{2}}}^{3}}{{(\sqrt{3375})}^{3}} \cdot 1325$

Step 1.2

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

$\frac{27^{3}}{{(\sqrt{3375})}^{3}} \cdot 1325$

Step 1.3

Raise $27$ to the power of $3$ .

$\frac{19683}{{(\sqrt{3375})}^{3}} \cdot 1325$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $3375$ as $15^{2} \cdot 15$ .

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Step 2.1.1

Factor $225$ out of $3375$ .

$\frac{19683}{{\sqrt{225 (15)}}^{3}} \cdot 1325$

Step 2.1.2

Rewrite $225$ as $15^{2}$ .

$\frac{19683}{{\sqrt{15^{2} \cdot 15}}^{3}} \cdot 1325$

Step 2.2

Pull terms out from under the radical.

$\frac{19683}{{(15 \sqrt{15})}^{3}} \cdot 1325$

Step 2.3

Apply the product rule to $15 \sqrt{15}$ .

$\frac{19683}{15^{3} {\sqrt{15}}^{3}} \cdot 1325$

Step 2.4

Raise $15$ to the power of $3$ .

$\frac{19683}{3375 {\sqrt{15}}^{3}} \cdot 1325$

Step 2.5

Rewrite ${\sqrt{15}}^{3}$ as $\sqrt{15^{3}}$ .

$\frac{19683}{3375 \sqrt{15^{3}}} \cdot 1325$

Step 2.6

Raise $15$ to the power of $3$ .

$\frac{19683}{3375 \sqrt{3375}} \cdot 1325$

Step 2.7

Rewrite $3375$ as $15^{2} \cdot 15$ .

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Step 2.7.1

Factor $225$ out of $3375$ .

$\frac{19683}{3375 \sqrt{225 (15)}} \cdot 1325$

Step 2.7.2

Rewrite $225$ as $15^{2}$ .

$\frac{19683}{3375 \sqrt{15^{2} \cdot 15}} \cdot 1325$

Step 2.8

Pull terms out from under the radical.

$\frac{19683}{3375 (15 \sqrt{15})} \cdot 1325$

Step 2.9

Multiply $15$ by $3375$ .

$\frac{19683}{50625 \sqrt{15}} \cdot 1325$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $25$ .

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Step 3.1.1

Factor $25$ out of $50625 \sqrt{15}$ .

$\frac{19683}{25 (2025 \sqrt{15})} \cdot 1325$

Step 3.1.2

Factor $25$ out of $1325$ .

$\frac{19683}{25 (2025 \sqrt{15})} \cdot (25 (53))$

Step 3.1.3

Cancel the common factor.

$\frac{19683}{25 (2025 \sqrt{15})} \cdot (25 \cdot 53)$

Step 3.1.4

Rewrite the expression.

$\frac{19683}{2025 \sqrt{15}} \cdot 53$

Step 3.2

Combine $\frac{19683}{2025 \sqrt{15}}$ and $53$ .

$\frac{19683 \cdot 53}{2025 \sqrt{15}}$

Step 3.3

Multiply $19683$ by $53$ .

$\frac{1043199}{2025 \sqrt{15}}$

Step 3.4

Cancel the common factor of $1043199$ and $2025$ .

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Step 3.4.1

Factor $81$ out of $1043199$ .

$\frac{81 (12879)}{2025 \sqrt{15}}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $81$ out of $2025 \sqrt{15}$ .

$\frac{81 (12879)}{81 (25 \sqrt{15})}$

Step 3.4.2.2

Cancel the common factor.

$\frac{81 \cdot 12879}{81 (25 \sqrt{15})}$

Step 3.4.2.3

Rewrite the expression.

$\frac{12879}{25 \sqrt{15}}$

Step 4

Multiply $\frac{12879}{25 \sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{12879}{25 \sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{12879}{25 \sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{12879 \sqrt{15}}{25 \sqrt{15} \sqrt{15}}$

Step 5.2

Move $\sqrt{15}$ .

$\frac{12879 \sqrt{15}}{25 (\sqrt{15} \sqrt{15})}$

Step 5.3

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{12879 \sqrt{15}}{25 ({\sqrt{15}}^{1} \sqrt{15})}$

Step 5.4

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{12879 \sqrt{15}}{25 ({\sqrt{15}}^{1} {\sqrt{15}}^{1})}$

Step 5.5

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

$\frac{12879 \sqrt{15}}{25 {\sqrt{15}}^{1 + 1}}$

Step 5.6

Add $1$ and $1$ .

$\frac{12879 \sqrt{15}}{25 {\sqrt{15}}^{2}}$

Step 5.7

Rewrite ${\sqrt{15}}^{2}$ as $15$ .

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Step 5.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15}$ as $15^{\frac{1}{2}}$ .

$\frac{12879 \sqrt{15}}{25 {(15^{\frac{1}{2}})}^{2}}$

Step 5.7.2

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

$\frac{12879 \sqrt{15}}{25 \cdot 15^{\frac{1}{2} \cdot 2}}$

Step 5.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{12879 \sqrt{15}}{25 \cdot 15^{\frac{2}{2}}}$

Step 5.7.4

Cancel the common factor of $2$ .

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Step 5.7.4.1

Cancel the common factor.

$\frac{12879 \sqrt{15}}{25 \cdot 15^{\frac{2}{2}}}$

Step 5.7.4.2

Rewrite the expression.

$\frac{12879 \sqrt{15}}{25 \cdot 15^{1}}$

Step 5.7.5

Evaluate the exponent.

$\frac{12879 \sqrt{15}}{25 \cdot 15}$

Step 6

Cancel the common factor of $12879$ and $15$ .

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Step 6.1

Factor $3$ out of $12879 \sqrt{15}$ .

$\frac{3 (4293 \sqrt{15})}{25 \cdot 15}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $25 \cdot 15$ .

$\frac{3 (4293 \sqrt{15})}{3 (25 \cdot 5)}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (4293 \sqrt{15})}{3 (25 \cdot 5)}$

Step 6.2.3

Rewrite the expression.

$\frac{4293 \sqrt{15}}{25 \cdot 5}$

Step 7

Multiply $25$ by $5$ .

$\frac{4293 \sqrt{15}}{125}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4293 \sqrt{15}}{125}$

Decimal Form:

$133.01374004 \dots$