How do I operate exponents on fractions?

[Deagonx]

I'm rather confused on how to operate exponents on fractions. For example

(4/3)^-1

or

(4/3)^1

Please explain?

 

[SteamKing]

Exponents on fractions work the same as on non-fractional quantities.

Thus, (4/3)^1 = 4/3; (4/3)^2 = 16/9 , etc.

(4/3)^-1 = 1/(4/3) = 3/4; (4/3)^-2 = 1/(4/3)^2 = 9/16, etc.

 

[Averki]

You could distribute the exponent into the parentheses to both the numerator and denominator of the fraction. For example:

\frac{4^-^1}{3^-^1} = \frac{\frac{1}{4}}{\frac{1}{3}}}

Now multiply the fraction in the numerator by \frac{3}{3} and the fraction in the denominator by \frac{4}{4}

This will yield the fraction \frac{\frac{3}{12}}{\frac{4}{12}}

Finally, multiply both the numerator and denominator by 12, which will yield the final fraction of \frac{3}{4}

If you plug (\frac{4}{3})^-^1 into your calculator, you will get the fraction \frac{3}{4}

I hope this helps.