Pre-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.

Tap for more steps...

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

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

Tap for more steps...

Step 5.1

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

$- \frac{27}{125} ({(- 1)}^{2} {(\frac{5}{3})}^{2})$

Step 5.2

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

$- \frac{27}{125} ({(- 1)}^{2} \frac{5^{2}}{3^{2}})$

Step 6

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move ${(- 1)}^{2}$ .

${(- 1)}^{2} \cdot - 1 \frac{27}{125} \frac{5^{2}}{3^{2}}$

Step 6.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

Tap for more steps...

Step 6.2.1

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

${(- 1)}^{2} \cdot {(- 1)}^{1} \frac{27}{125} \frac{5^{2}}{3^{2}}$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(- 1)}^{2 + 1} \frac{27}{125} \frac{5^{2}}{3^{2}}$

Step 6.3

Add $2$ and $1$ .

${(- 1)}^{3} \frac{27}{125} \frac{5^{2}}{3^{2}}$

Step 7

Evaluate the exponents.

Tap for more steps...

Step 7.1

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

${(- 1)}^{3} \frac{27}{125} \frac{25}{3^{2}}$

Step 7.2

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

${(- 1)}^{3} \frac{27}{125} \frac{25}{9}$

Step 7.3

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

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

Step 8

Cancel the common factor of $9$ .

Tap for more steps...

Step 8.1

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

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

Step 8.2

Factor $9$ out of $- 27$ .

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

Step 8.3

Cancel the common factor.

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

Step 8.4

Rewrite the expression.

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

Step 9

Cancel the common factor of $25$ .

Tap for more steps...

Step 9.1

Factor $25$ out of $125$ .

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

Step 9.2

Cancel the common factor.

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

Step 9.3

Rewrite the expression.

$\frac{- 3}{5}$

Step 10

Move the negative in front of the fraction.

$- \frac{3}{5}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$