Question

All of the following expressions are equal except _____

Answer 1

Answer:

4^5/4^2

Step-by-step explanation:

4^5/4^2 = 4^3

All the others are equal to 1 / 4^3.

Answer 2

Answer:

All the following expressions are equal expect

$\dfrac{4^{5}}{4^2}$

Step-by-step explanation:

$\sf \dfrac{1}{4^3}\\\\\dfrac{4^2}{4^5}=\dfrac{1}{4^{5-2}}}=\dfrac{1}{4^3}\\\\4^{-3}=\dfrac{1}{4^{3}}$

But,

     $\sf \dfrac{4^5}{4^2}=4^{5-2}=4^{3} \ which \ differs \ from \ other \ three \expressions$

Exponnet law:

$\sf a^{-m} =\dfrac{1}{a^m}\\\\ \dfrac{a^{m}}{a^{n}}=a^{m-n} , \ if \ m > n\\\\\dfrac{a^{m}}{a^n}=\dfrac{1}{a^{n-m}}, \ if \ m < n$