What is sqrt((4/3)^{2x-3)} ?

The solution to sqrt((4/3)^{2x-3)} is (2^{2x-3}}{3^{\frac{2x-3)/2}}

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simplify sqrt((4/3)^{2x-3)}

simplify

(\frac{4}{3})^{2 x - 3}

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

Solution steps

(\frac{4}{3})^{2 x - 3}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((\frac{4}{3})^{2 x - 3})^{\frac{1}{2}}

Apply exponent rule:

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

= (\frac{4}{3})^{(2 x - 3) \frac{1}{2}}

Simplify

(2 x - 3) \frac{1}{2} : \frac{2 x - 3}{2}

= (\frac{4}{3})^{\frac{2 x - 3}{2}}

Apply exponent rule:

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

= \frac{4 ^{\frac{2 x - 3}{2}}}{3 ^{\frac{2 x - 3}{2}}}

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

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

\frac{4 ^{0}}{0 !} \cdot e^{- 4}

3 \cdot 1 0^{- 3} (\frac{7 π}{- 15})

60.656 e^{- 0.0892 (5)}

0.4 \cdot 1 0^{- 2}

What is sqrt((4/3)^{2x-3)} ?
The solution to sqrt((4/3)^{2x-3)} is (2^{2x-3}}{3^{\frac{2x-3)/2}}