Algebra I
Name: ________________________________________
7.1 Zero and Negative Exponents
Objectives:
To simplify expressions with zero and negative exponents
Warm Up: Complete without a calculator!
1. a) Fill in the chart with the value of the power in standard form.
x
2x
5x
10 x
4
3
2
b) Look at the values that you used to replace the blanks. What pattern do you see as
you go down each column?
2. Use the pattern you described in 1b to complete the table below. (If you use a
calculator, leave your answers as a fraction)
x
1
0
-1
-2
2x
5x
10 x
The patterns that you found on the first page illustrate the definitions of zero and negative
exponents.
Zero as an Exponent Property: __________________________________________________________________________
Example 1):
50 =
(-2)0 =
(1.023)0 =
Negative Exponent Property: ____________________________________________________________________________
Example 2):
6-4 =
(-8)-1 =
Quick Check:
Simplifying Powers: What is the simplified form of each expression?
1) 9−2
2) (−3.6)0
3) 4−3
4) (−5)0
5) (−4)−2
Simplifying an Exponential Expression:
An algebraic expression is in simplest form when powers with a variable base _____________________
_______________________________________________________________________________________________________________
Example 3): Simplify each expression (GOAL: Eliminate all negative exponents)
a) 4𝑥 −3 𝑦
1
b) 𝑤−4
c) 7𝑠 −4 𝑡 2
d)
𝑛−5
𝑣2
e) 𝑠 0 𝑟 −3
Quick Check: Simplify Each Expression
1) 5𝑎3 𝑏 −2
1
2) 𝑥 −5
3) 5𝑏𝑐 −3
2
4) 𝑎−3
5)
𝑛−5
𝑚2
Evaluating an Exponential Expression: Always simplify the expression before substituting
values in for the variables
Example 4): Evaluate 3m 2t -2 for m = 2 and t = -3 (Hint: always use parenthesis!!)
Example 5): Evaluate
𝑛−1
𝑤2
for n = - 2 and w = 5
Quick Check: Evaluate each expression for n = -2 and w = 5
a)n-3w0
n-2
b) 3
w
w0
c) 4
n
d)
1
nw-2
Using an Exponential Expression:
Example 6) A population of marine bacteria doubles every hour under controlled laboratory
conditions. The number of bacteria is modeled by the expression 1000 ∙ 2ℎ , where h is the
number of hours after a scientist measures the population size. Evaluate the expression for h=0
and h= -3. What does each value of the expression represent in the situation?
Quick Check: A population of insects triples every week. The number of insects is modeled by
the expression 5400 ∙ 3𝑤 , where w is the number of weeks after the population was measured.
Evaluate the expression for w= -2, w= 0, and w = 1. What does the value of the expression mean
in the situation?