Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Apply the product rule to $- \frac{5}{3}$ .

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

Step 2.2

Apply the product rule to $\frac{5}{3}$ .

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

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

$- \frac{3125}{3^{5}} \cdot {(\frac{3}{4})}^{2}$

Step 3.3

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

$- \frac{3125}{243} \cdot {(\frac{3}{4})}^{2}$

Step 3.4

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

$- \frac{3125}{243} \cdot \frac{3^{2}}{4^{2}}$

Step 3.5

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

$- \frac{3125}{243} \cdot \frac{9}{4^{2}}$

Step 3.6

Raise $4$ to the power of $2$ .

$- \frac{3125}{243} \cdot \frac{9}{16}$

Step 4

Cancel the common factor of $9$ .

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Step 4.1

Move the leading negative in $- \frac{3125}{243}$ into the numerator.

$\frac{- 3125}{243} \cdot \frac{9}{16}$

Step 4.2

Factor $9$ out of $243$ .

$\frac{- 3125}{9 (27)} \cdot \frac{9}{16}$

Step 4.3

Cancel the common factor.

$\frac{- 3125}{9 \cdot 27} \cdot \frac{9}{16}$

Step 4.4

Rewrite the expression.

$\frac{- 3125}{27} \cdot \frac{1}{16}$

Step 5

Multiply $\frac{- 3125}{27}$ by $\frac{1}{16}$ .

$\frac{- 3125}{27 \cdot 16}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $27$ by $16$ .

$\frac{- 3125}{432}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{3125}{432}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3125}{432}$

Decimal Form:

$- 7.2337\overline{962}$

Mixed Number Form:

$- 7 \frac{101}{432}$