Basic Math Examples

$\frac{2}{3} \cdot {(\frac{2}{3})}^{2} - \frac{9}{10}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{2}{3}$ by ${(\frac{2}{3})}^{2}$ by adding the exponents.

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Step 1.1.1

Multiply $\frac{2}{3}$ by ${(\frac{2}{3})}^{2}$ .

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Step 1.1.1.1

Raise $\frac{2}{3}$ to the power of $1$ .

${(\frac{2}{3})}^{1} \cdot {(\frac{2}{3})}^{2} - \frac{9}{10}$

Step 1.1.1.2

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

${(\frac{2}{3})}^{1 + 2} - \frac{9}{10}$

Step 1.1.2

Add $1$ and $2$ .

${(\frac{2}{3})}^{3} - \frac{9}{10}$

Step 1.2

Apply the product rule to $\frac{2}{3}$ .

$\frac{2^{3}}{3^{3}} - \frac{9}{10}$

Step 1.3

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

$\frac{8}{3^{3}} - \frac{9}{10}$

Step 1.4

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

$\frac{8}{27} - \frac{9}{10}$

Step 2

To write $\frac{8}{27}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{8}{27} \cdot \frac{10}{10} - \frac{9}{10}$

Step 3

To write $- \frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$\frac{8}{27} \cdot \frac{10}{10} - \frac{9}{10} \cdot \frac{27}{27}$

Step 4

Write each expression with a common denominator of $270$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{8}{27}$ by $\frac{10}{10}$ .

$\frac{8 \cdot 10}{27 \cdot 10} - \frac{9}{10} \cdot \frac{27}{27}$

Step 4.2

Multiply $27$ by $10$ .

$\frac{8 \cdot 10}{270} - \frac{9}{10} \cdot \frac{27}{27}$

Step 4.3

Multiply $\frac{9}{10}$ by $\frac{27}{27}$ .

$\frac{8 \cdot 10}{270} - \frac{9 \cdot 27}{10 \cdot 27}$

Step 4.4

Multiply $10$ by $27$ .

$\frac{8 \cdot 10}{270} - \frac{9 \cdot 27}{270}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 \cdot 10 - 9 \cdot 27}{270}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $8$ by $10$ .

$\frac{80 - 9 \cdot 27}{270}$

Step 6.2

Multiply $- 9$ by $27$ .

$\frac{80 - 243}{270}$

Step 6.3

Subtract $243$ from $80$ .

$\frac{- 163}{270}$

Step 7

Move the negative in front of the fraction.

$- \frac{163}{270}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{163}{270}$

Decimal Form:

$- 0.6\overline{037}$