Algebra Examples

${(3^{- \frac{6}{5}} \cdot 3^{\frac{9}{5}})}^{- \frac{3}{2}}$

Step 1

Multiply $3^{- \frac{6}{5}}$ by $3^{\frac{9}{5}}$ 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.

${(3^{- \frac{6}{5} + \frac{9}{5}})}^{- \frac{3}{2}}$

Step 1.2

Combine the numerators over the common denominator.

${(3^{\frac{- 6 + 9}{5}})}^{- \frac{3}{2}}$

Step 1.3

Add $- 6$ and $9$ .

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

Step 2

Multiply the exponents in ${(3^{\frac{3}{5}})}^{- \frac{3}{2}}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2

Multiply $\frac{3}{5} (- \frac{3}{2})$ .

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Step 2.2.1

Multiply $\frac{3}{5}$ by $\frac{3}{2}$ .

$3^{- \frac{3 \cdot 3}{5 \cdot 2}}$

Step 2.2.2

Multiply $3$ by $3$ .

$3^{- \frac{9}{5 \cdot 2}}$

Step 2.2.3

Multiply $5$ by $2$ .

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

Step 3

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

$\frac{1}{3^{\frac{9}{10}}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3^{\frac{9}{10}}}$

Decimal Form:

$0.37204105 \dots$