Question

9 Apply index law three to simplify each of the following. a (m2) b 6(p^)

Answer 1

Answer:

• See the law and the hypothetical example below.

Explanation:

The index law that you are dealing with is:

            $\dfrac{a^m}{a^n}=a^{m-n}$

It is used when you have the quotient of powers with the same base.

To show you how to use that rule, let's work an example

Simplify:

              $\dfrac{9a(m^2)}{6b(m^4)}$

Factor 9 as 3² and 6 as 2×3:

         $\dfrac{3^2a(m^2)}{2\times 3b(m^4)}$

Group the factor with equal base:

           $\dfrac{a}{2b}\times \dfrac{3^2}{3}\times \dfrac{m^2}{m^4}$

Use the index law:

            $\dfrac{a}{2b}\times {3^{(2-1)}}\times m^{(2-4)}\\\\\\ \dfrac{a}{2b}\times3\times m^{-2}\\\\\\\dfrac{3a}{2bm^2}$

Note that it was used an additional rule:           $a^{-n}=\dfrac{1}{a^n}$

Thus,           $m^{-2}=\dfrac{1}{m^2}$