Rational Exponents

**Courtx33333** · May 2nd 2012, 02:08 PM

The surface area S, in square units, of a sphere with volume V, in cubic units, is given by the formula S = π^1/3(6V)^2/3. What is the surface area of a sphere with volume 4/3 mi^3?
Write your answer in terms of π^1/3 ? Please explain how to do this!

**Prove It** · May 2nd 2012, 02:19 PM

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.

**Courtx33333** · May 2nd 2012, 02:54 PM

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

**Prove It** · May 2nd 2012, 04:14 PM

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:

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

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