Simplify 11^(2a) ÷ 11^5: Exponential Division Problem

Question

Insert the corresponding expression:

112a115= \frac{11^{2a}}{11^5}=

Video Solution

Solution Steps

00:00 Simply
00:02 According to the laws of exponents, dividing exponents with equal bases (A)
00:05 equals the same base (A) to the power of the exponents' difference (M-N)
00:08 We will use this formula in our exercise
00:10 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we apply the Power of a Quotient Rule for Exponents, which states that for any non-zero base a a and integers m m and n n , the expression aman=amn \frac{a^m}{a^n} = a^{m-n} . In this case, our base a a is 11.

Given the expression 112a115 \frac{11^{2a}}{11^5} , let's simplify it using the rule:

  • The numerator is 112a 11^{2a} .
  • The denominator is 115 11^5 .

Applying the rule:

112a115=112a5 \frac{11^{2a}}{11^5} = 11^{2a-5}

Thus, the expression simplifies to 112a5 11^{2a-5} .

So, the solution to the question is: 112a5 11^{2a-5}

Answer

112a5 11^{2a-5}