Question

If g = $t^{\frac{2}{3}}+4t^{\frac{-1}{2}}$, what is the value of g when t = 64?

• A. $\frac{31}{2}$
• B. $\frac{33}{2}$
• C. 16
• D. $\frac{257}{16}$

Answer 1

Answer: (B)

$\frac{33}{2}$

$g=t^{\frac{2}{3}}+4t^{\frac{-1}{2}}=t^{\frac{2}{3}}+4\times \frac{1}{t^{\frac{1}{2}}}=(64{)}^{\frac{2}{3}}+4\times \frac{1}{{64}^{\frac{1}{2}}}=(4^3{)}^{\frac{2}{3}}+4\times \frac{1}{(8^2{)}^{\frac{1}{2}}}=4^2+4\times \frac{1}{8^{2\times \frac{1}{2}}}=4^2+\frac{4}{8}=16+\frac{1}{2}=\frac{33}{2}$