# Simple exponential equation help

• Jan 6th 2011, 02:06 PM
youngb11
Simple exponential equation help
Seems like a simple question but I need some help understanding the steps.

How would I write this as a power of 4:

$$\sqrt[3]{8}^5$$

Steps to tackle such problems would be greatly appreciated!
• Jan 6th 2011, 02:08 PM
Ackbeet
How could you write 8 as a power of 4?
• Jan 6th 2011, 02:15 PM
youngb11
Quote:

Originally Posted by Ackbeet
How could you write 8 as a power of 4?

Aah okay, I get it. Thanks a lot!
• Jan 6th 2011, 02:16 PM
Ackbeet
You're welcome. Have a good one!
• Jan 6th 2011, 02:24 PM
pickslides
Quote:

Originally Posted by Ackbeet
How could you write 8 as a power of 4?

Interesting, I was always taught $\displaystyle \sqrt[3]{8}^5 = (8^\frac{1}{3}})^5 = 2^5 = 32 = 2\times 16 = 2 \times 4^2$
• Jan 6th 2011, 02:27 PM
Ackbeet
Ah, but that doesn't quite cut it, I think. The whole number is a power of 4. So you'd have

$8^{\frac{5}{3}}=(4^{\frac{3}{2}})^{\frac{5}{3}}=4^ {\frac{5}{2}}.$