Basic Math Examples

${(\frac{3}{2})}^{- 5} \div {(\frac{8}{3} - 2)}^{7}$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{3}{2})}^{- 5}}{{(\frac{8}{3} - 2)}^{7}}$

Step 2

Move ${(\frac{3}{2})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(\frac{8}{3} - 2)}^{7} {(\frac{3}{2})}^{5}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{{(\frac{8}{3} - 2 \cdot \frac{3}{3})}^{7} {(\frac{3}{2})}^{5}}$

Step 3.2

Combine $- 2$ and $\frac{3}{3}$ .

$\frac{1}{{(\frac{8}{3} + \frac{- 2 \cdot 3}{3})}^{7} {(\frac{3}{2})}^{5}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{1}{{(\frac{8 - 2 \cdot 3}{3})}^{7} {(\frac{3}{2})}^{5}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $- 2$ by $3$ .

$\frac{1}{{(\frac{8 - 6}{3})}^{7} {(\frac{3}{2})}^{5}}$

Step 3.4.2

Subtract $6$ from $8$ .

$\frac{1}{{(\frac{2}{3})}^{7} {(\frac{3}{2})}^{5}}$

Step 3.5

Apply the product rule to $\frac{2}{3}$ .

$\frac{1}{\frac{2^{7}}{3^{7}} {(\frac{3}{2})}^{5}}$

Step 3.6

Apply the product rule to $\frac{3}{2}$ .

$\frac{1}{\frac{2^{7}}{3^{7}} \cdot \frac{3^{5}}{2^{5}}}$

Step 3.7

Raise $2$ to the power of $7$ .

$\frac{1}{\frac{128}{3^{7}} \cdot \frac{3^{5}}{2^{5}}}$

Step 3.8

Raise $3$ to the power of $7$ .

$\frac{1}{\frac{128}{2187} \cdot \frac{3^{5}}{2^{5}}}$

Step 3.9

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

$\frac{1}{\frac{128}{2187} \cdot \frac{243}{2^{5}}}$

Step 3.10

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

$\frac{1}{\frac{128}{2187} \cdot \frac{243}{32}}$

Step 4

Simplify terms.

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Step 4.1

Multiply $\frac{128}{2187}$ by $\frac{243}{32}$ .

$\frac{1}{\frac{128 \cdot 243}{2187 \cdot 32}}$

Step 4.2

Multiply.

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Step 4.2.1

Multiply $128$ by $243$ .

$\frac{1}{\frac{31104}{2187 \cdot 32}}$

Step 4.2.2

Multiply $2187$ by $32$ .

$\frac{1}{\frac{31104}{69984}}$

Step 4.3

Cancel the common factor of $31104$ and $69984$ .

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Step 4.3.1

Factor $7776$ out of $31104$ .

$\frac{1}{\frac{7776 (4)}{69984}}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $7776$ out of $69984$ .

$\frac{1}{\frac{7776 \cdot 4}{7776 \cdot 9}}$

Step 4.3.2.2

Cancel the common factor.

$\frac{1}{\frac{7776 \cdot 4}{7776 \cdot 9}}$

Step 4.3.2.3

Rewrite the expression.

$\frac{1}{\frac{4}{9}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{9}{4})$

Step 6

Multiply $\frac{9}{4}$ by $1$ .

$\frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$