Basic Math Examples

$\frac{{(- \frac{3}{4})}^{5} \cdot {(\frac{8}{9})}^{5}}{{(\frac{27}{2})}^{5}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $- \frac{3}{4}$ .

$\frac{{(- 1)}^{5} {(\frac{3}{4})}^{5} {(\frac{8}{9})}^{5}}{{(\frac{27}{2})}^{5}}$

Step 1.2

Apply the product rule to $\frac{8}{9}$ .

$\frac{{(- 1)}^{5} {(\frac{3}{4})}^{5} \frac{8^{5}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.3

Combine exponents.

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Step 1.3.1

Combine $\frac{8^{5}}{9^{5}}$ and ${(- 1)}^{5}$ .

$\frac{\frac{8^{5} {(- 1)}^{5}}{9^{5}} {(\frac{3}{4})}^{5}}{{(\frac{27}{2})}^{5}}$

Step 1.3.2

Combine $\frac{8^{5} {(- 1)}^{5}}{9^{5}}$ and ${(\frac{3}{4})}^{5}$ .

$\frac{\frac{8^{5} {(- 1)}^{5} {(\frac{3}{4})}^{5}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the product rule to $\frac{3}{4}$ .

$\frac{\frac{8^{5} {(- 1)}^{5} \frac{3^{5}}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.2

Combine exponents.

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Step 1.4.2.1

Combine $8^{5}$ and $\frac{3^{5}}{4^{5}}$ .

$\frac{\frac{{(- 1)}^{5} \frac{8^{5} \cdot 3^{5}}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.2.2

Combine ${(- 1)}^{5}$ and $\frac{8^{5} \cdot 3^{5}}{4^{5}}$ .

$\frac{\frac{\frac{{(- 1)}^{5} (8^{5} \cdot 3^{5})}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.3

Simplify the numerator.

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Step 1.4.3.1

Raise $- 1$ to the power of $5$ .

$\frac{\frac{\frac{- 1 \cdot 8^{5} \cdot 3^{5}}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.3.2

Raise $8$ to the power of $5$ .

$\frac{\frac{\frac{- 1 \cdot 32768 \cdot 3^{5}}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.3.3

Raise $3$ to the power of $5$ .

$\frac{\frac{\frac{- 1 \cdot 32768 \cdot 243}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.3.4

Combine exponents.

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Step 1.4.3.4.1

Multiply $- 1$ by $32768$ .

$\frac{\frac{\frac{- 32768 \cdot 243}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.3.4.2

Multiply $- 32768$ by $243$ .

$\frac{\frac{\frac{- 7962624}{4^{5}}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.4

Raise $4$ to the power of $5$ .

$\frac{\frac{\frac{- 7962624}{1024}}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.4.5

Divide $- 7962624$ by $1024$ .

$\frac{\frac{- 7776}{9^{5}}}{{(\frac{27}{2})}^{5}}$

Step 1.5

Raise $9$ to the power of $5$ .

$\frac{\frac{- 7776}{59049}}{{(\frac{27}{2})}^{5}}$

Step 1.6

Cancel the common factor of $- 7776$ and $59049$ .

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Step 1.6.1

Factor $243$ out of $- 7776$ .

$\frac{\frac{243 (- 32)}{59049}}{{(\frac{27}{2})}^{5}}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $243$ out of $59049$ .

$\frac{\frac{243 \cdot - 32}{243 \cdot 243}}{{(\frac{27}{2})}^{5}}$

Step 1.6.2.2

Cancel the common factor.

$\frac{\frac{243 \cdot - 32}{243 \cdot 243}}{{(\frac{27}{2})}^{5}}$

Step 1.6.2.3

Rewrite the expression.

$\frac{\frac{- 32}{243}}{{(\frac{27}{2})}^{5}}$

Step 1.7

Move the negative in front of the fraction.

$\frac{- \frac{32}{243}}{{(\frac{27}{2})}^{5}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{27}{2}$ .

$\frac{- \frac{32}{243}}{\frac{27^{5}}{2^{5}}}$

Step 2.2

Raise $27$ to the power of $5$ .

$\frac{- \frac{32}{243}}{\frac{14348907}{2^{5}}}$

Step 2.3

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

$\frac{- \frac{32}{243}}{\frac{14348907}{32}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{32}{243} \cdot \frac{32}{14348907}$

Step 4

Multiply $- \frac{32}{243} \cdot \frac{32}{14348907}$ .

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Step 4.1

Multiply $\frac{32}{14348907}$ by $\frac{32}{243}$ .

$- \frac{32 \cdot 32}{14348907 \cdot 243}$

Step 4.2

Multiply $32$ by $32$ .

$- \frac{1024}{14348907 \cdot 243}$

Step 4.3

Multiply $14348907$ by $243$ .

$- \frac{1024}{3486784401}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1024}{3486784401}$

Decimal Form:

$- 2.93680331 \cdot 10^{- 7}$