Basic Math Examples

${(- \frac{4}{5})}^{2} \cdot \frac{15}{8}$

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

${(- 1)}^{2} {(\frac{4}{5})}^{2} \cdot \frac{15}{8}$

Step 1.2

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

${(- 1)}^{2} \frac{4^{2}}{5^{2}} \cdot \frac{15}{8}$

Step 2

Simplify the expression.

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Step 2.1

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

$1 \frac{4^{2}}{5^{2}} \cdot \frac{15}{8}$

Step 2.2

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

$\frac{4^{2}}{5^{2}} \cdot \frac{15}{8}$

Step 3

Combine.

$\frac{4^{2} \cdot 15}{5^{2} \cdot 8}$

Step 4

Simplify the expression.

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Step 4.1

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

$\frac{16 \cdot 15}{5^{2} \cdot 8}$

Step 4.2

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

$\frac{16 \cdot 15}{25 \cdot 8}$

Step 4.3

Multiply $16$ by $15$ .

$\frac{240}{25 \cdot 8}$

Step 4.4

Multiply $25$ by $8$ .

$\frac{240}{200}$

Step 5

Cancel the common factor of $240$ and $200$ .

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Step 5.1

Factor $40$ out of $240$ .

$\frac{40 (6)}{200}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $40$ out of $200$ .

$\frac{40 \cdot 6}{40 \cdot 5}$

Step 5.2.2

Cancel the common factor.

$\frac{40 \cdot 6}{40 \cdot 5}$

Step 5.2.3

Rewrite the expression.

$\frac{6}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{5}$

Decimal Form:

$1.2$

Mixed Number Form:

$1 \frac{1}{5}$