Question

How do you prove that B(t)=1067.1 radical of 3/t divided by t to the 3rd power is actually the same thing as B(t)= 1067.1t to the -2 2/3 power? I need step by step instructions so I can understand how to do it in the future.

Answer 1

If you mean this
\[1061.1\frac{\sqrt[3]{t}}{t^{3}}\]
then if you change the cube root to a fractional power,
\[1061.1\frac{t^{\frac{1}{3}}}{t^{3}}\]
you subtract powers, that is (1/3)-3= -2 1/3
you get
\[1061.1 t^{-2}t^{-\frac{2}{3}}\]
for example, or t^(-8/3) or 1/t^(8/3)

Answer 2

You are awesome, thank you!!