Simplify the Expression: a^a/a^b Using Exponent Rules

Question

Simplify the following:

aaab= \frac{a^a}{a^b}=

Video Solution

Solution Steps

00:00 Simply
00:03 When dividing powers with equal bases
00:07 The power of the result equals the difference of the exponents
00:11 We'll use this formula in our exercise, and subtract the exponents
00:14 And this is the solution to the question

Step-by-Step Solution

Since a division operation between two terms with identical bases is required, we will use the power property to divide terms with identical bases:

cmcn=cmn \frac{c^m}{c^n}=c^{m-n} Note that using this property is only possible when the division is performed between terms with identical bases.

We return to the problem and apply the mentioned power property:

aaab=aab \frac{a^a}{a^b}=a^{a-b} Therefore, the correct answer is option D.

Answer

aab a^{a-b}