Basic Math Examples

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

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 $- \frac{3}{5}$ .

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

Step 1.2

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

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

Step 2

Raise $- 1$ to the power of $2$ .

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

Step 3

Multiply $\frac{3^{2}}{5^{2}}$ by $1$ .

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

Step 4

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

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

Step 5

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

$\frac{9}{25} {(- \frac{4}{5})}^{2}$

Step 6

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

Tap for more steps...

Step 6.1

Apply the product rule to $- \frac{4}{5}$ .

$\frac{9}{25} ({(- 1)}^{2} {(\frac{4}{5})}^{2})$

Step 6.2

Apply the product rule to $\frac{4}{5}$ .

$\frac{9}{25} ({(- 1)}^{2} \frac{4^{2}}{5^{2}})$

Step 7

Combine fractions.

Tap for more steps...

Step 7.1

Raise $- 1$ to the power of $2$ .

$\frac{9}{25} (1 \frac{4^{2}}{5^{2}})$

Step 7.2

Multiply $\frac{4^{2}}{5^{2}}$ by $1$ .

$\frac{9}{25} \cdot \frac{4^{2}}{5^{2}}$

Step 7.3

Combine.

$\frac{9 \cdot 4^{2}}{25 \cdot 5^{2}}$

Step 7.4

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

$\frac{9 \cdot 16}{25 \cdot 5^{2}}$

Step 8

Simplify the denominator.

Tap for more steps...

Step 8.1

Rewrite $25$ as $5^{2}$ .

$\frac{9 \cdot 16}{5^{2} \cdot 5^{2}}$

Step 8.2

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

$\frac{9 \cdot 16}{5^{2 + 2}}$

Step 8.3

Add $2$ and $2$ .

$\frac{9 \cdot 16}{5^{4}}$

Step 9

Simplify the expression.

Tap for more steps...

Step 9.1

Multiply $9$ by $16$ .

$\frac{144}{5^{4}}$

Step 9.2

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

$\frac{144}{625}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{144}{625}$

Decimal Form:

$0.2304$