Question

How to simplify fractions with negative exponents in the denominator and numerator?

Answer 1

Answer:

$\displaystyle\frac{x^{-a}}{x^{-b}} = x^{b-a}$

Step-by-step explanation:

We have to write the rule  to simplify fractions with negative exponents in the denominator and numerator.

If we have positive exponents, the simplification takes place as following:

$\displaystyle\frac{x^a}{x^b} = x^{a-b}$

The powers of the same base of numerator and denominator are subtracted.

In case of negative exponents, the simplification takes place in the following manner:

$\displaystyle\frac{x^{-a}}{x^{-b}} = x^{-a-(-b)} = x^{-a+b} = x^{b-a}$

The powers of the same base of denominator and numerator are subtracted.