Algebra 1 Common Core Student Edition, Grade 8-9

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