What is (3/4)^{1.5}*(2/3)^{2.5} ?

The solution to (3/4)^{1.5}*(2/3)^{2.5} is (3^{1.5}*2^{2.5})/(4^{1.5)*3^{2.5}}

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simplify (3/4)^{1.5}*(2/3)^{2.5}

simplify

(\frac{3}{4})^{1.5} \cdot (\frac{2}{3})^{2.5}

\frac{3 ^{1.5} \cdot 2 ^{2.5}}{4 ^{1.5} \cdot 3 ^{2.5}}

Decimal Notation

0.23570 \dots

Solution steps

(\frac{3}{4})^{1.5} (\frac{2}{3})^{2.5}

Apply exponent rule:

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

(\frac{3}{4})^{1.5} = \frac{3 ^{1.5}}{4 ^{1.5}}

= \frac{3 ^{1.5}}{4 ^{1.5}} (\frac{2}{3})^{2.5}

Apply exponent rule:

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

(\frac{2}{3})^{2.5} = \frac{2 ^{2.5}}{3 ^{2.5}}

= \frac{3 ^{1.5}}{4 ^{1.5}} \cdot \frac{2 ^{2.5}}{3 ^{2.5}}

\frac{3 ^{1.5}}{4 ^{1.5}} \cdot \frac{2 ^{2.5}}{3 ^{2.5}} = \frac{3 ^{1.5} \cdot 2 ^{2.5}}{4 ^{1.5} \cdot 3 ^{2.5}}

= \frac{3 ^{1.5} \cdot 2 ^{2.5}}{4 ^{1.5} \cdot 3 ^{2.5}}

y^{2} - 4 y + 13 = 0

\frac{a}{4} - \frac{5}{6} = - \frac{1}{2}

3 x^{2} - x = \frac{23}{2}

lo g_{2} (\frac{1}{x}) + lo g_{2} (\frac{1}{x ^{2}})

- 8 x - 27 < 5

What is (3/4)^{1.5}*(2/3)^{2.5} ?
The solution to (3/4)^{1.5}*(2/3)^{2.5} is (3^{1.5}*2^{2.5})/(4^{1.5)*3^{2.5}}