Finite Math Examples

${(9^{2} \cdot 2^{3} \cdot \sqrt[3]{2} \cdot 27^{- 27})}^{2}$

Step 1

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

${(81 \cdot 2^{3} \cdot \sqrt[3]{2} \cdot 27^{- 27})}^{2}$

Step 2

Raise $2$ to the power of $3$ .

${(81 \cdot 8 \cdot \sqrt[3]{2} \cdot 27^{- 27})}^{2}$

Step 3

Multiply $81$ by $8$ .

${(648 \cdot \sqrt[3]{2} \cdot 27^{- 27})}^{2}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(648 \sqrt[3]{2} \cdot \frac{1}{27^{27}})}^{2}$

Step 5

Multiply $648 \sqrt[3]{2} \frac{1}{27^{27}}$ .

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Step 5.1

Combine $\frac{1}{27^{27}}$ and $648$ .

${(\frac{648}{27^{27}} \sqrt[3]{2})}^{2}$

Step 5.2

Combine $\frac{648}{27^{27}}$ and $\sqrt[3]{2}$ .

${(\frac{648 \sqrt[3]{2}}{27^{27}})}^{2}$

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $\frac{648 \sqrt[3]{2}}{27^{27}}$ .

$\frac{{(648 \sqrt[3]{2})}^{2}}{{(27^{27})}^{2}}$

Step 6.2

Apply the product rule to $648 \sqrt[3]{2}$ .

$\frac{648^{2} {\sqrt[3]{2}}^{2}}{{(27^{27})}^{2}}$

Step 7

Simplify the numerator.

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Step 7.1

Raise $648$ to the power of $2$ .

$\frac{419904 {\sqrt[3]{2}}^{2}}{{(27^{27})}^{2}}$

Step 7.2

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

$\frac{419904 \sqrt[3]{2^{2}}}{{(27^{27})}^{2}}$

Step 7.3

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

$\frac{419904 \sqrt[3]{4}}{{(27^{27})}^{2}}$

Step 8

Multiply the exponents in ${(27^{27})}^{2}$ .

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Step 8.1

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

$\frac{419904 \sqrt[3]{4}}{27^{27 \cdot 2}}$

Step 8.2

Multiply $27$ by $2$ .

$\frac{419904 \sqrt[3]{4}}{27^{54}}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{419904 \sqrt[3]{4}}{27^{54}}$

Decimal Form:

$3.38995092 \cdot 10^{- 72}$