Finding k when 8√8 = 8^k

[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

 

[Hootenanny]

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

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

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

 

[thomas49th]

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

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

cheerz

 

[Hootenanny]

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

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

cheerz

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