Basic Math Examples

$\frac{1}{3} \cdot {(\frac{1}{3})}^{2} - \frac{5}{27}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{3}$ by ${(\frac{1}{3})}^{2}$ by adding the exponents.

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Step 1.1.1

Multiply $\frac{1}{3}$ by ${(\frac{1}{3})}^{2}$ .

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Step 1.1.1.1

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

${(\frac{1}{3})}^{1} \cdot {(\frac{1}{3})}^{2} - \frac{5}{27}$

Step 1.1.1.2

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

${(\frac{1}{3})}^{1 + 2} - \frac{5}{27}$

Step 1.1.2

Add $1$ and $2$ .

${(\frac{1}{3})}^{3} - \frac{5}{27}$

Step 1.2

Apply the product rule to $\frac{1}{3}$ .

$\frac{1^{3}}{3^{3}} - \frac{5}{27}$

Step 1.3

One to any power is one.

$\frac{1}{3^{3}} - \frac{5}{27}$

Step 1.4

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

$\frac{1}{27} - \frac{5}{27}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 - 5}{27}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $5$ from $1$ .

$\frac{- 4}{27}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{4}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{27}$

Decimal Form:

$- 0.\overline{148}$