Question

Given the expression 12 over 12 to the third power. Part A: Explain how the Quotient of Powers was used to simplify the expression. (6 points) Part B: Simplify the expression. (4 points)

Answer 1

We have the following fractional expression:

12

-------- is the same as

12^3

12^1

-------

12^3

We want to simplify this expression. To do so, we need the formula for exponents as follows:

x^a / x^b = x^(a-b).

In this particular problem we have

12^1 / 12^3, and know by this formula that the correct result is 12^(1-3), or 12^(-2), which is equivalent to 1 / 144.