1. Warm Up #7 Simplify each expression. 1. (–2)3 –8 2. 52 – 34 –56
1. (–2)3 –8
2. 52 – 34
–56
3. A gigabyte is about 103 megabytes. A music player
has 4 gigabytes of memory. About how many
megabytes is this?
4000 megabytes

2. Use properties of Exponents
5.1
Use properties of Exponents
Objective: Simplify expressions involving powers

4. Evaluate numerical expressions
EXAMPLE 1
Evaluate numerical expressions 7.
(– )2
= (– 4)2 (25)2
Power of a product property =
Power of a power property =
= 16,384
Simplify and evaluate power. 9.
115
118 –1
118
115 =
Negative exponent property
= 118 – 5
Quotient of powers property
= 113
= 1331
Simplify and evaluate power.

5. Use scientific notation in real life
EXAMPLE 2
Use scientific notation in real life
A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 square kilometers. About how many locusts are in such a swarm?
= 85,000,
= ( )( )
Write in scientific notation.
= ( )( )
Use multiplication properties. =
Product of powers property =
Write 10.2 in scientific notation. =
Product of powers property

6. GUIDED PRACTICE
for Examples 1 and 2
Evaluate the expression.
(42 )3
4096
ANSWER
2. (–8)(–8)3
ANSWER
4096 3.
2 3 9 8
ANSWER
729

7. GUIDED PRACTICE
for Examples 1 and 2
– 4
18.

8. EXAMPLE 3 Simplify expressions 5. b–4b6b7 = b–4 + 6 + 7 = b9 10.
Product of powers property
10.
s–2 –3 s3
(s–2 )–3
( s3 )–3 =
Power of a quotient property =
s 6
s–9
Power of a power property
= s15
Negative exponent property
m4n –5
2n–5
= 8m4n –5 – (–5)
Quotient of powers property
= 8m4n0= 8m4
Zero exponent property

9. EXAMPLE 4
Standardized Test Practice #16
(x–3y3)2
x5y6 =
(x–3)2(y3)2
x5y6
x –6y6
x5y6 =
= x –6 – 5y6 – 6
= x–11y0 = 1
x11

10. GUIDED PRACTICE
for Examples 3, 4, and 5
Simplify the expression.
6. x–6x5 x–3
(7y2z5)(y–4z–1)
x–4
7y-2z4

11. GUIDED PRACTICE
for Examples 3, 4, and 5
14.
s 3 2
t–4
15.
x4y–
x3y6

12. Classwork/Homework pages 333-334 (3-39 multiples of 3, and #52)