Question

the expression \[b^{-3\2} , b>0 \] is the equivalent to?

Answer 1

$a^\frac{m}{n}=\sqrt[n]{a^m}\\\\a^{-n}=\dfrac{1}{a^n}\\----------\\\\b^{-\frac{3}{2}}=\left(\dfrac{1}{b}\right)^\frac{3}{2}=\left(\dfrac{1}{b}\right)^{1\frac{1}{2}}=\left(\dfrac{1}{b}\right)^{1+\frac{1}{2}}=\dfrac{1}{b}\cdot\left(\dfrac{1}{b}\right)^\frac{1}{2}=\dfrac{1}{b}\cdot\dfrac{1}{b^\frac{1}{2}}\\\\=\dfrac{1}{b}\cdot\dfrac{1}{\sqrt{b}}=\dfrac{1}{b\sqrt{b}}=\dfrac{1\cdot\sqrt{b}}{b\sqrt{b}\cdot\sqrt{b}}=\dfrac{\sqrt{b}}{b\cdot b}=\dfrac{\sqrt{b}}{b^2}$

$Answer:\boxed{b^{-\frac{3}{2}}=\frac{\sqrt{b}}{b^2}}$

Answer 2

The expression \[b^{-3\2} , b>0 \]  is the equivalent to; 

=1/b3/2=1/b3−−√