Math Help - Rational Exponents

1. Re: Rational Exponents

I assume the volume is \displaystyle \begin{align*} \frac{4}{3}\pi^3 \end{align*}. Substitute this as \displaystyle \begin{align*} V \end{align*} into the formula \displaystyle \begin{align*} S = \pi ^{\frac{1}{3}}\left(6V\right)^{\frac{2}{3}} \end{align*} and simplify.

2. Re: Rational Exponents

When you substitute that in as V, it comes out as 57.81 ? How do you write that in terms of π^1/3 ? Please show the steps in solving

3. Re: Rational Exponents

Originally Posted by Courtx33333
When you substitute that in as V, it comes out as 57.81 ? How do you write that in terms of π^1/3 ? Please show the steps in solving
You need to use the following index laws:

\displaystyle \begin{align*} a^m \cdot a^n &= a^{m + n} \\ \\ \left(a^n\right)^p &= a^{n \cdot p} \\ \\ \left(a \cdot b \right)^n &= a^n \cdot b^n \end{align*}