How do you simplify
the expression?
Use the definition of
negative exponent to
rewrite the expression
with only positive
exponent s.
When you evaluate an exponential expression, you can simplify the expression before
substituting values for the variables.
Pr o b lem 3 Evalu at in g an Exp o n en t ial Exp ressio n
What is the value of 3s3t~2 for s = 2 and t = —31
Method 1 Simplify first. Method 2 Substitute first.
3s3r 2 = 3W _
t2
3(2)3
(~~3)2
_ 24 _„2
9 3
3s 3 r 2 = 3(2) 3 (—3)-2
3(2)3
( 3)
24 =
9
^j) Got It? 3. What is the value of each expression in parts (a)-(d) for n = - 2 and w = 51
a. n 4w° b-^Sr d.
wz
C.
we nw 1
e. Reasoning Is it easier to evaluate n°w° for n = —2 and w = 3 by
simplifying first or by substituting first? Explain.
Pro b lem 4 Using an Exp o n en t ial Exp ressio n
Po p u l at i o n Gr o w t h 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?
1000 • 2h models the
population.
Val ues of t he expressi on
for h = 0 and h = -3
Pbn
Su b st i t u t e e ac h v a l u e o f h into
the expression and simplify.
1000 • 2h = 1000 • 2 ,o' Su b st i t u t e 0 f o r h.
= 1000 • 1 = 1000 Si m p l i f y.
The value of the expression for h = 0 is 1000. There were 1000 bacteria at the time the
scientist measured the population.
Su b st i t u t e - 3 f o r h.
= 1000 • i = 125 Si m p l i f y.
1000 • 2h = 1000 • 2~3
The value of the expression for h = - 3 is 125. There were 125 bacteria 3 h before the
scientist measured the population.
420 Ch a p t e r 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s