Question

Please help me with this problem. I'm stuck!!

Answer 1

$\bf S(t)=4\pi \left( \cfrac{3}{8}t^4 \right)^2\impliedby \textit{distributing the exponent} \\\\\\ S(t)=4\pi \left( \cfrac{3^2}{8^2}t^{4\cdot 2} \right)\implies S(t)=4\pi \cdot \cfrac{9t^8}{64}\implies S(t)=\cfrac{4}{64}\cdot \cfrac{9\pi t^8}{1} \\\\\\ S(t)=\cfrac{1}{16}\cdot \cfrac{9\pi t^8}{1}\implies S(t)=\cfrac{9\pi t^8}{16}$