Algebra 1 SOL A.2 Laws of Exponents, Scientific Notation WS
Ms. Bradley
Name: ________________________________________ Date: __________________ Block: _______
Laws of Exponents:

am ∙ an = am+n
am

= am-n
an

(am)n = amn

(ab)m = ambm
Scientific Notation

Use LAWS OF EXPONENTS to multiply,
divide, or raise a number in scientific
notation to a power

DON’T EXPAND THE SCIENTIFIC
NOTATION NUMBER!!

Multiply/Divide/Raise to a power the
numbers NOT in scientific notation

Multiply/Divide/Raise to a power the
power terms

Put back in scientific notation if
necessary!!

Example: (5.2 x 108) x (7.8 x 10-2)
m




am
a 
   m
b
b
a0 = 1
1
a-n = n
a
1
an = -n
a
o = (5.2)(7.8) (108)(10-2)
o = 40.56 x 106
o = 4.056 x 107
Exercises: Simplify the expressions. Write all answers using POSITIVE exponents.
1) 15-4(158)
2) a7(a8)(a)
3) (3m4n6)(2mn)0(2m2n)
4) 10-8∙105
5) (-1x5y6)10
7)
x 5 y
x2
6)
 28a 6 b 3 c 5
7a 11b 5 c 5
8)
y3
y -2
(2ab 7 )3
9)
(a 4 b 2 )5
10) (5m3n)(-2mn3)
11) (7ab)(-a4b3)2(2a5b6)-1
 3x 7 y 4
12)  3 5
 2x y
 25x -17 y 24 z  2
13) 
20 -6 5
 4x y z
15)
1
 x 20
7
x



0
14)
16)



4
x 4 x 9
x5
2x 3
2x 4
3x 

2 3
2x 4
Algebra 1 SOL A.2 Laws of Exponents, Scientific Notation WS
Ms. Bradley Page 2
Convert to scientific notation:
17)
415, 620
18)
19)
3,412,200
20)
0.08014
0.0000456
Convert to standard (decimal) form:
21)
8.12 x 10-4
22)
1.722 x 107
23)
1.211 x 10-2
24)
6.02 x 1023
Order the numbers from least to greatest:
25) 0.16; 2.5x10-3; 1.04x10-3; 0.0985
Evaluate the expressions:
26)
(6 x
108)(5
29) (7.3 x
x
10-2)
10-5)(5.8
x
102)
27)
4.5  10 5
9  10  2
30)
1.235  10 4
9.5  10 7
28) (2 x 10-5)5
31) (1.4 x 103)2
32) The images on a computer screen are made up of more than 5,000 pixels, or dots, per
square inch. How many pixels are there on a computer screen that measures 108
square inches? Use scientific notation to solve the problem, and in your answer.