Basic Math Examples

${(2 \frac{4}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 1

Convert $2 \frac{4}{5}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

${(2 + \frac{4}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 1.2

Add $2$ and $\frac{4}{5}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

${(2 \cdot \frac{5}{5} + \frac{4}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 1.2.2

Combine $2$ and $\frac{5}{5}$ .

${(\frac{2 \cdot 5}{5} + \frac{4}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 1.2.3

Combine the numerators over the common denominator.

${(\frac{2 \cdot 5 + 4}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

${(\frac{10 + 4}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 1.2.4.2

Add $10$ and $4$ .

${(\frac{14}{5})}^{- 2} \cdot {(3 - 0.25)}^{3}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{5}{14})}^{2} \cdot {(3 - 0.25)}^{3}$

Step 3

Apply the product rule to $\frac{5}{14}$ .

$\frac{5^{2}}{14^{2}} \cdot {(3 - 0.25)}^{3}$

Step 4

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

$\frac{25}{14^{2}} \cdot {(3 - 0.25)}^{3}$

Step 5

Raise $14$ to the power of $2$ .

$\frac{25}{196} \cdot {(3 - 0.25)}^{3}$

Step 6

Subtract $0.25$ from $3$ .

$\frac{25}{196} \cdot {2.75}^{3}$

Step 7

Raise $2.75$ to the power of $3$ .

$\frac{25}{196} \cdot 20.796875$

Step 8

Multiply $\frac{25}{196} \cdot 20.796875$ .

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Step 8.1

Combine $\frac{25}{196}$ and $20.796875$ .

$\frac{25 \cdot 20.796875}{196}$

Step 8.2

Multiply $25$ by $20.796875$ .

$\frac{519.921875}{196}$

Step 9

Divide $519.921875$ by $196$ .

$2.65266262$