Question

Find the quotient of (11 ^ 18)/(11 ^ 3)

Answer 1

Answer:

The first choice, $11^{15}$.

Step-by-step explanation:

The numerator, $11^{18}$, is equivalent to eighteen "$11$" multiplied together:

$11^{18} = \underbrace{11 \times 11 \times 11 \times 11 \times \cdots \times 11 \times 11}_{\text{ 18 in total}}$.

On the other hand, the denominator, $11^{3}$, is equivalent to three "$11$" multiplied with one another:

$11^{3} = 11 \times 11 \times 11$.

Dividing $11^{18}$ by $11^{3}$ would eliminate three "$11$" from the numerator:

$\begin{aligned}& \frac{11^{18}}{11^{3}} \\ =\; & \frac{(11 \times 11 \times 11) \times \overbrace{11 \times \cdots \times 11}^{\text{ (18 - 3) in total}}}{(11 \times 11 \times 11)} \\ =\; & \overbrace{11 \times \cdots \times 11}^{\text{ 15 in total}} \\ =\; & 11^{15}\end{aligned}$.

In general, dividing an expression by $y^{b}$ ($y \ne 0$) is equivalent to multiplying that expression by $y^{-b}$.

For example, in this question, dividing $11^{18}$ by $11^{3}$ would be equivalent to multiplying $11^{18}\!$ by $11^{-3}$. In other words:

$\begin{aligned}& \frac{11^{18}}{11^{3}} \\ =\; & 11^{18} \times 11^{-3} \\ =\; & 11^{18 - 3} \\ =\; & 11^{15}\end{aligned}$.