Question

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

Answer 1

The first choice,
`11^(15)`.

Explanation:

The numerator,
`11^(18)`, is equivalent to eighteen "
`11`" multiplied together:

`11^(18) = \underbrace{11 * 11 * 11 * 11 * \cdots * 11 * 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 * 11 * 11`.

Dividing
`11^(18)` by
`11^(3)` would eliminate three "
`11`" from the numerator:

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

In general, dividing an expression by
`y^(b)` (
`y \\e 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}& (11^(18))/(11^(3)) \\ =\; & 11^(18) * 11^(-3) \\ =\; & 11^(18 - 3) \\ =\; & 11^(15)\end{aligned}`.