Answer
$\text{ approximately }2,045.0 \text{ calories}$
Work Step by Step
Using the given function, $
B(w)=70w^{3/4}
,$ then
\begin{array}{l}\require{cancel}
B(w)=70(90)^{3/4}
.\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}
B(w)=70\sqrt[4]{90^3}
.\end{array}
Using the laws of exponents and the properties of radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
B(w)=70\sqrt[4]{(3^2\cdot10)^3}
\\
B(w)=70\sqrt[4]{3^{2(3)}\cdot10^{3}}
\\
B(w)=70\sqrt[4]{3^{6}\cdot10^{3}}
\\
B(w)=70\sqrt[4]{3^{4}\cdot3^2\cdot10^{3}}
\\
B(w)=70\cdot3\sqrt[4]{3^2\cdot10^{3}}
\\
B(w)=210\sqrt[4]{9\cdot1000}
\\
B(w)=210\sqrt[4]{9000}
\\
B(w)\approx2045.0
.\end{array}
Hence, the BMR, $B(w),$ for a person who weighs $90$ kilograms is $
\text{ approximately }2,045.0 \text{ calories}
.$
