Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify the expression.

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Step 2.1

Raise $- 1$ to the power of $3$ .

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

Step 2.2

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

$- \frac{27}{5^{3}} {(\frac{5}{3})}^{2}$

Step 2.3

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

$- \frac{27}{125} {(\frac{5}{3})}^{2}$

Step 2.4

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

$- \frac{27}{125} \cdot \frac{5^{2}}{3^{2}}$

Step 2.5

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

$- \frac{27}{125} \cdot \frac{25}{3^{2}}$

Step 2.6

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

$- \frac{27}{125} \cdot \frac{25}{9}$

Step 3

Cancel the common factor of $9$ .

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Step 3.1

Move the leading negative in $- \frac{27}{125}$ into the numerator.

$\frac{- 27}{125} \cdot \frac{25}{9}$

Step 3.2

Factor $9$ out of $- 27$ .

$\frac{9 (- 3)}{125} \cdot \frac{25}{9}$

Step 3.3

Cancel the common factor.

$\frac{9 \cdot - 3}{125} \cdot \frac{25}{9}$

Step 3.4

Rewrite the expression.

$\frac{- 3}{125} \cdot 25$

Step 4

Cancel the common factor of $25$ .

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Step 4.1

Factor $25$ out of $125$ .

$\frac{- 3}{25 (5)} \cdot 25$

Step 4.2

Cancel the common factor.

$\frac{- 3}{25 \cdot 5} \cdot 25$

Step 4.3

Rewrite the expression.

$\frac{- 3}{5}$

Step 5

Move the negative in front of the fraction.

$- \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$