Algebra Examples

$3^{2} \cdot 3^{- 3} \cdot 3^{\frac{2}{3}}$

Step 1

Multiply $3^{2}$ by $3^{- 3}$ by adding the exponents.

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Step 1.1

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

$3^{2 - 3} \cdot 3^{\frac{2}{3}}$

Step 1.2

Subtract $3$ from $2$ .

$3^{- 1} \cdot 3^{\frac{2}{3}}$

Step 2

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

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Step 2.1

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

$3^{- 1 + \frac{2}{3}}$

Step 2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$3^{- 1 \cdot \frac{3}{3} + \frac{2}{3}}$

Step 2.3

Combine $- 1$ and $\frac{3}{3}$ .

$3^{\frac{- 1 \cdot 3}{3} + \frac{2}{3}}$

Step 2.4

Combine the numerators over the common denominator.

$3^{\frac{- 1 \cdot 3 + 2}{3}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 1$ by $3$ .

$3^{\frac{- 3 + 2}{3}}$

Step 2.5.2

Add $- 3$ and $2$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{\frac{1}{3}}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3^{\frac{1}{3}}}$

Decimal Form:

$0.69336127 \dots$