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.