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Popular >

simplify (2/3)^{3/2}

Solution

simplify

(\frac{2}{3})^{\frac{3}{2}}

Solution

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

+1

Decimal Notation

0.54433 \dots

Solution steps

(\frac{2}{3})^{\frac{3}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{2 ^{\frac{3}{2}}}{3 ^{\frac{3}{2}}}

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

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

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

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

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Frequently Asked Questions (FAQ)

What is (2/3)^{3/2} ?
The solution to (2/3)^{3/2} is (2*2^{1/2})/(3*3^{1/2)}