definition of let b represent any real number and n represent a positive integer. then, n factors of...
TRANSCRIPT
Definition of Let b represent any real number and n represent a positive integer. Then,
n factors of b
nb
...nb b b b b b
Expression Base Exponent Result
6² 6 2 (6)(6) = 36
(-½)³ -½ 3 (½)(½)(½) =
0.8⁴ 0.8 4 (.8)(.8)(.8)(.8) = .4096
1
8
5 is the base to the exponent 4
45
41 5
1 5 5 5 5 625
4( 5)
Multiply -1 times four factors of 5
Parentheses indicate that -5 is the base to the exponent 4.
Multiply four factors of -5= (-5)(-5)(-5)(-5)
= 625
Substitute a = 2
25a Use parentheses to substitute a number for a variable.
= 5 ( )²
2
Simplify
2
= 5(4)
= 20
Substitute a = 2
2(5 )aUse parentheses to substitute a number for a variable.
= [5( )]²
2
Simplify inside the parentheses first
2
= (10)²
= 100
Substitute a = 2 b = -3
25ab Use parentheses to substitute a number for a variable.
= 5( ) ( )²
2
Simplify inside the parentheses first
2
= 5(2)(9)
= 100
-3
-3
multiply
Tip: In the expression 5ab² the exponent, 2 applies only to the variable b. The constant 5 and the variable a both have an implied exponent of 1.
Substitute a = 2 b = -3
2( )a b
= (a + b )²
2
Simplify inside the parentheses first
2
= [(2) + (-3)]²
= (-1)²
-3
-3
= 1
Avoiding Mistakes: Be sure to follow the order of operations. It would be incorrect to square the terms within the parentheses before adding.
Multiplication of Like Bases
Assume that a≠ 0 is a real number and that m and n represent positive integers. Then, Property 1
5 2 7( )( ) ( )x x x x x x x x x x x x x x x x x
m n m na a a
5 2 5 2 7x x x x
Division of Like Bases
Assume that a ≠ 0 is a real number and that m and n represent positive integers such that m > n. Then,
Property 2:
53
2 1
x x x x x x x x xx
x x x
mm n
n
aa
a
55 2 3
2
xx x
x
3 4
3 4 7
w w
w w
(x∙x∙x)(x∙x∙x∙x)
Add the exponents
3 4
3 4 7
2 2
2 2 128 (2∙2∙2∙2∙2∙2∙2)
Add the exponents ( the base is unchanged).
6 2
6
4
4 t
t
t
t
(t∙t∙t∙t∙t∙t) (t∙t∙t∙t)
Subtract the exponents
2
6
4
4
65 5
5
5
5 2
5∙5∙5∙5∙5∙5 5∙5∙5∙5
Subtract the exponents ( the base is unchanged).
6 3 99 3 6
3 3
6 3
3
z z
z
z zz z
z z
Subtract the
exponents
7 77 3 4
2 1
2
3
7
10 1010 10 10,000
10 1
0
0
0
1
10 1
Note that 10 is equivalent to 10¹
Add the exponents in the denominator ( the base is unchanged).
Add the exponents in the numerator ( the base is unchanged).
Subtract the exponents
Simplify
(3p²q⁴)(2pq⁵)
Apply the associative and commutative properties of multiplication to group coefficients and like bases
=(3∙2)(p²p)(q⁴q⁵)
Add the exponents when multiplying like bases.
2 1 4 5(3 2)( )p q
Simplify
3 96p q