Algebra Examples

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

Step 1

Move $3^{\frac{- 3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Move the negative in front of the fraction.

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

Step 3

Multiply $- - \frac{3}{2}$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.2

Multiply $\frac{3}{2}$ by $1$ .

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor of $3$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.18224727 \dots$