Simple exponential equation help

**youngb11** · January 6th 2011, 01:06 PM

Seems like a simple question but I need some help understanding the steps.

How would I write this as a power of 4:

[Math]\sqrt[3]{8}^5[/tex]

Steps to tackle such problems would be greatly appreciated!

**Ackbeet** · January 6th 2011, 01:08 PM

How could you write 8 as a power of 4?

**youngb11** · January 6th 2011, 01:15 PM

Originally Posted by Ackbeet

How could you write 8 as a power of 4?

Aah okay, I get it. Thanks a lot!

**Ackbeet** · January 6th 2011, 01:16 PM

You're welcome. Have a good one!

**pickslides** · January 6th 2011, 01:24 PM

Originally Posted by Ackbeet

How could you write 8 as a power of 4?

Interesting, I was always taught $\displaystyle \sqrt[3]{8}^5 = (8^\frac{1}{3}})^5 = 2^5 = 32 = 2\times 16 = 2 \times 4^2$

**Ackbeet** · January 6th 2011, 01:27 PM

Ah, but that doesn't quite cut it, I think. The whole number is a power of 4. So you'd have

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

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