Expressing fractions as powers?

[MadmanMurray]

Expressing fractions as powers??

How would you go about expressing this 127/squareroot(5) as a power of 5? I got a copy of last years exams to use for revision and practice and its full of stuff I don't know how to do. This one happens to be a multiple choice and the possible answers are 5 to the power of A:3 1/2, B: 6, C: -1 1/2, D: -3

I know most of the laws of indices but I am stuck here.

 

[mutton]

Are you sure the question says 127/squareroot(5)?

You can check that none of the answers match this value.

 

[HallsofIvy]

A number in the denominator corresponds to a number in the numerator with a negative power. However, sqrt(5) in the denominator is 5^-1/2, not -1 1/2 or -3. If the denominator were $\sqrt{5^3}= \sqrt{125}$, then the exponent would be -3/2= -1 1/2.

 

[MadmanMurray]

Sorry it was 125 over square root of 5 not 127. I have no idea how to solve this.

I considered actually dividing the denominator into the numerator then using logs to convert the answer to a power of 5 but that method seems way too impractical to be the commonly used method.

HallsofIvy I don't fully get what you said about the denominator and the numerator.

 

[mutton]

Spelling it out,

$$\frac{125}{\sqrt{5}} = \frac{5^3}{5^{1/2}} = 5^{3 - 1/2} = 5^{5/2}$$

 

[MadmanMurray]

Thanks a lot.