Things to Learn

  • Know the definition of a number raised to a negative exponent.
  • Simplify and write equivalent expressions that contain negative exponents.

Exploring Negative Exponents Warm-Up

Exploring Negative Exponents

Defining Negative Exponents
[shc_shortcode class=”shc_mybox”]For any nonzero number `x`, and for any positive integer `n`, we define `x^(−n)` as `1/(x^n)`
Note that this definition of negative exponents says `x^(−1)` is just the reciprocal of `x` — `1/x`.
As a consequence of the definition, for a nonnegative `x` and all integers `b` we get `x^(-b) = 1/(x^b)`.[/shc_shortcode]

Exercise and Practice(PDF printable)

[shc_shortcode class=”shc_mybox”]
We accept that for nonzero numbers `x` and `y` and all integers `a` and `b`,
`x^a * x^b = x^(a+b)`
`(x^b)^a = x^(ab)`
`(xy)^a = x^ay^a`.

We claim:
`x^a/x^b = x^(a-b)` for all integers `a, b`.
`(x/y)^a = x^a/y^a` for any integer `a`.
[/shc_shortcode]

Before You Go