Question

Which of the following would be equivalent to 11 to the 8th power over 11 to the 3rd power?

A)11 to the 7th power over 11 to the 7th power
B)11 ⋅ 114
C)11 to the 0 power over 11 to the 5th power
D)110

Answer 1

none of the above. 11^8/11^3 is 11^5 since you will just subtract exponents. The numerical value is 161051
although you should have an option that either is 11^5 or equals 11^5 like 11^15/11^10 for example

Answer 2

Option: B is the correct answer.

`B)\ 11\cdot 11^4`

Explanation:

We are given a numerical expression as:

11 to the 8th power over 11 to the 3rd power.

i.e. mathematically it is given by:

`(11^8)/(11^3)`

Now, we know that if the numerator and the denominator terms are power terms such that both the terms are of same base then the resultant is the same base and the exponent of the base is: exponent of numerator minus exponent of denominator.

i.e.

`(a^m)/(a^n)=a^(m-n)`

Here we have:

`a=11,\ m=8\ and\ n=3`

Hence, we get:

`(11^8)/(11^3)=11^(8-3)`

i.e.

`(11^8)/(11^3)=11^5`

Now, this could also be written as:

`(11^8)/(11^3)=11\cdot 11^4`

( since,

`a^m\cdot a^n=a^(m+n)\\\\i.e.\\\\11^1\cdot 11^4=11^(4+1)=11^5` )