Download Study Guide Algebra I Chapter 8, pages 430

Study Guide Algebra I
Chapter 8, pages 430-459
Know the exponent rules and be able to use them.
a m • a n = a m+n
(ab) n = a n b n
(a n ) m = a nm
a0 = 1
1
a−n = n
a
am
a
n
= a m−n
REMEMBER:
(negative number) odd = negative number
€
(negative number) even = positive number
€
REMEMBER: If there
is no exponent written then the exponent is 1.
€
1
x=x
3xy 2 = 31 x1 y 2
€
1. Be able to simplify expressions or numbers raised to the zero power
REMEMBER: anything to the zero power is 1
150 = 1
-(8x)0 = -1  (8x)0 = 1 but the – sign is not raised to the 0 power
 4 0
−  = 1
 3
€ 2. Be able to simplify expressions or numbers to the negative power
REMEMBER: a negative exponent on the top goes to the bottom and becomes
positive and a negative exponent on the bottom goes to the top and becomes
positive.
Examples:
1.)
m 2 n −3
the m2 stays on the top because it’s exponent is +
the n-3 goes to the bottom because it’s exponent is –
2 −3
m n
€
1 1
2.) € 3−2 = 2 =
3€ 9
€
3.)
9−1
=
m2
n3
NOTE: the negative goes away when you move it.
move the 32 to the bottom
flip the fraction because they are both negative exponents
3−2
32 9
=
= =1
3−2 91 9
9−1
€
4.)
€
7s0 t −5
−1
2 m
2
the 7 & s0 stay on the top (positive exponents) and the m2
stays on the bottom (positive exponents)
−5
the t goes to the bottom and the 2−1 and goes to the top
(negative exponents)
€
7s0 t −5
7 •1• 2
14
=
=
2−1 m 2€ m 2 t 5
m 2t 5
€
REMEMBER: s0 = 1
€ 3. Be able to evaluate an expression for given values
REMEMBER: rewrite your expression first to get rid of any negative
exponents then substitute the values. Put ( ) around negative numbers.
Example:
Evaluate each expression for r = -3 and s = 5.
1
1
1
s−2  rewrite  2  substitute  2 =
25
s
5
5r 3
5(−3) 3 5(−27)
=
= −27
5r 3s−1  rewrite  1  substitute 
€
€
5
s
51
€
 −4 2
0
 r s
you don’t have to do€anything to this problem
 6−8 r 4 s−7  €

the answer is 1
€
€ (REMEMBER: anything to the 0 power is 1)
4. Be able to simplify power to power expressions using the exponent rules
Simplify the following expressions:
1.)
(−2m−5n)−2
1
€
(−2m−5n) 2
1
2
(−2) m
€
n
multiply exponents
square (-2) & move the m
−10
to the top
m10
4n 2
€
2.)
€
€
€
€ 3.)
€
€
€
€
€
−10 2
negative exponent (-2) moves the entire
expression to the denominator
(5a 3b 2 ) 3
5 3 a 3•3b 2•3
75a 9b 6
(2a−2b 3 ) 2 (ab 2 ) 3
2 2 a−2•2b 3•2 a1•3b 2•3
4a−4 b 6 a 3b 6
4a−4 a 3b 6b 6
4a−1b12
distribute the exponent 3 to each element
distribute the exponents 2 & 3
multiply the exponents
rearrange terms
add your exponents
4b12
a
move a−1 to the denominator
€
€ 5. Be able to simplify expressions with division using exponent rules
REMEMBER:
1.)
am
a
5y 2
y5
€
5y −3
5
€
n
= a m−n
subtract the y exponents
move y
−3
to the denominator the 5 stays on top
y3
€
€ 2.)
y −2
y5
y −7
1
€
€
3.)
€
€
€
€
subtract the exponents
move the y −7 denominator
y7
a 3b 2c −4
€
a−2b 5c −9
a 3−(−2)b 2−5c −4−(−9) subtract your exponents
a 5b−3c 5
move the b term to the denominator
5 5
a c
b3
€
REMEMBER:
(-2)2 = 4
and
-22 = -4
have different answers
notice ( ) they make the difference
(-2)2 means (-2)(-2) which is 4
-22 means –(2)(2) which is -4