# Surd as power

1. May 12, 2007

### thomas49th

$$8\sqrt{8}$$ can be written in the form $$8^{k}$$

Find the value of k

I'm positive is a really easy question I though that k = 1/8, but that is wrong.
What is the method to answer this question.. I used trial and error and got k = 3/2, but what is the proper way?

Thanks

2. May 12, 2007

### Hootenanny

Staff Emeritus
Well what is a if $\sqrt{8} = 8^{a}$?

What is b if $8 = 8^{b}$?

What is $8^a\cdot8^b$?

3. May 12, 2007

### thomas49th

$$8^{\frac{2}{2}} x 8^{\frac{1}{2}}$$

= $$8^{\frac{3}{2}}$$

cheerz

4. May 12, 2007

### Hootenanny

Staff Emeritus
Pleasure