Basic Math Examples

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

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

Step 1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

Tap for more steps...

Step 1.1

Apply the product rule to

- \frac{4}{5}

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

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

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

Step 1.2

Apply the product rule to

\frac{4}{5}

$\frac{4}{5}$ .

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

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

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

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

Step 2

Multiply

- 1

$- 1$ by

{(- 1)}^{2}

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

Tap for more steps...

Step 2.1

Move

{(- 1)}^{2}

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

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

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

Step 2.2

Multiply

{(- 1)}^{2}

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

- 1

$- 1$ .

Tap for more steps...

Step 2.2.1

Raise

- 1

$- 1$ to the power of

1

$1$ .

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

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

Step 2.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

Step 3

Raise

4

$4$ to the power of

2

$2$ .

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

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

Step 4

Raise

5

$5$ to the power of

2

$2$ .

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

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

Step 5

Raise

- 1

$- 1$ to the power of

3

$3$ .

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

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

Step 6

Multiply

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

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

Tap for more steps...

Step 6.1

Multiply

\frac{16}{25}

$\frac{16}{25}$ by

\frac{4}{5}

$\frac{4}{5}$ .

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

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

Step 6.2

Multiply

16

$16$ by

4

$4$ .

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

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

Step 6.3

Multiply

25

$25$ by

5

$5$ .

- \frac{64}{125}

$- \frac{64}{125}$

- \frac{64}{125}

$- \frac{64}{125}$

Step 7

The result can be shown in multiple forms.

Exact Form:

- \frac{64}{125}

$- \frac{64}{125}$

Decimal Form:

- 0.512

$- 0.512$