Question

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

Answer 1

When simplifying fractions with negative exponents in the numerator and denominator, you can flip the construction and change the negative exponent to a positive exponent. If there is a negative exponent in the numerator, you can move it to the denominator by changing the sign. Remember to simplify the fractions by dividing common factors.

Step-by-step explanation:

When simplifying fractions with negative exponents in the numerator and denominator, you can flip the construction and change the negative exponent to a positive exponent. For example, if you have a fraction like x^(-2) / y^(-3), you can rewrite it as y^3 / x^2.

If you have a negative exponent in the numerator, you can move it to the denominator by changing the sign of the exponent. For example, z^(-4) / w can be written as 1 / (w * z^4).

Remember to simplify the fractions by dividing the numerator and denominator by any common factors. This will give you the final simplified fraction.

Answer 2

`\displaystyle(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(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(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.