Answer
$27$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
0.1^{3/2}\cdot90^{3/2}
,$ use the laws of exponents.
$\bf{\text{Solution Details:}}$
Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(0.1\cdot90)^{3/2}
\\\\=
9^{3/2}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt[]{9})^{3}
\\\\=
(3)^{3}
\\\\=
27
.\end{array}
