Basic Math Examples

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

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 $- \frac{4}{5}$ .

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

Step 1.2

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

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

${(- 1)}^{3} \frac{4}{5} \cdot \frac{16}{5^{2}}$

Step 4

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

${(- 1)}^{3} \frac{4}{5} \cdot \frac{16}{25}$

Step 5

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

$- \frac{4}{5} \cdot \frac{16}{25}$

Step 6

Multiply $- \frac{4}{5} \cdot \frac{16}{25}$ .

Tap for more steps...

Step 6.1

Multiply $\frac{16}{25}$ by $\frac{4}{5}$ .

$- \frac{16 \cdot 4}{25 \cdot 5}$

Step 6.2

Multiply $16$ by $4$ .

$- \frac{64}{25 \cdot 5}$

Step 6.3

Multiply $25$ by $5$ .

$- \frac{64}{125}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{64}{125}$

Decimal Form:

$- 0.512$