Answer
a) $16$; b) $(t+1)^{4/3}$; c) $81$; d) $x^{4/3}$
Work Step by Step
We are given the function:
$g(x)=x^{4/3}$
a) Compute $g(8)$:
$g(8)=8^{4/3}=(2^3)^{4/3}=2^4=16$
b) Compute $g(t+1)$:
$g(t+1)=(t+1)^{4/3}$
c) Compute $g(-27)$:
$g(-27)=(-27)^{4/3}=(-3^3)^{4/3}=(-3)^4=81$
d) Compute $g(-x)$:
$g(-x)=(-x)^{4/3}=x^{4/3}$
