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

Part B: Simplify the expression

Answer 1

Part A: You can subtract the exponents 1 and 3 to end up with 12^-2. Then, you can simplify it into a fraction.

Part B: 12 ^ -2 = 1 / (12^2) = 1 / 144 OR about 0.007

Answer 2

Part 1:
Before we begin, you need to remember the following rule:

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

The given expression is:

`(12)/(12^3)`

Since the base is the same in both numerator and denominator, we can apply the above rule. This means that:

`(12)/(12^3)` = 12¹⁻³ = 12⁻²

Part 2:
Before we begin, you need to remember the following rule:
x⁻ᵃ =
`(1)/(x^a)`

Now, from part 1, we simplified the expression into 12⁻²
Since the power is negative, we can apply the above rule.
This means that:
12⁻² =
`(1)/((12)^2) = (1)/(12*12) = (1)/(144)`

Hope this helps :)