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:
$\frac{x^a}{x^b} = x^{a-b}$

The given expression is:
$\frac{12}{12^3}$

Since the base is the same in both numerator and denominator, we can apply the above rule. This means that:
$\frac{12}{12^3}$ = 12¹⁻³ = 12⁻²

Part 2:
Before we begin, you need to remember the following rule:
x⁻ᵃ = $\frac{1}{x^a}$

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 = $\frac{1}{(12)^2} = \frac{1}{12*12} = \frac{1}{144}$

Hope this helps :)