If x + 1/16x = 1, then the value of 64 x^3 + 1/64^3 is
a)4
b)52
c)64
d)76
Is your question:
If $\displaystyle \displaystyle \begin{align*} x + \frac{1}{16}x = 1 \end{align*}$ then find the value of $\displaystyle \displaystyle \begin{align*} 64x^3 + \frac{1}{64}x^3 \end{align*}$
or
If $\displaystyle \displaystyle \begin{align*} x + \frac{1}{16x} = 1 \end{align*}$ then find the value of $\displaystyle \displaystyle \begin{align*} 64x^3 + \frac{1}{64x^3} \end{align*}$?
$\displaystyle \\1 = {\left( {x + \frac{1}{{16x}}} \right)^3}\\1 = {x^3} + \frac{{3x}}{{16}} + \frac{3}{{{{16}^2}x}} + \frac{1}{{{{16}^3}{x^3}}} \\1= \left( {{x^3} + \frac{1}{{{{16}^2}{x^3}}}} \right) + \frac{3}{{16}} \left( {x + \frac{1}{{16x}}} \right)$
Thus $\displaystyle \left( {{x^3} + \frac{1}{{{{16}^2}{x^3}}}} \right) = \frac{{13}}{{16}}$.
You finish.