Power of Products with like bases
105 x 102 =
105+2=107
Simplify the expression: (x3)6
x18
Apply the properties of exponents to write an equivalent expression: (x2y)(x4y)
x6y2
a number with an exponent of zero is always:
1
examples:
30= 1
4,6890= 1
Write 10-4 as a fraction.
1 / 104
(-5)3 x (-5)8 =
(-5)11
p48
Simplify: (x)(x8)
x9
Solve: 110
1
How do you make a number with a negative exponent positive?
Put your number with a negative exponent into a fraction with a numerator of 1
example:
x-2 -> 1 / x2
When given a problem in the format of n2 x n7, what do you do with the exponents to solve the problem?
you add the exponents together
ex: n2 x n 7 = n9
When given a problem such as (x6)2, what do you do with the exponents to solve the problem?
you multiply the exponents together
ex: (x6)2= x6x2= x12
When given a problem such as (xy)3, what do you do with the exponent to solve the problem?
you distribute the exponent to each of the variables in the parenthesis
ex: (x3)(y3)
When given a number to the zero power, what is always the answer?
1
Write an expression equivalent to w-7 / w-4.
w-3 or 1 / w3
Write an equivalent expression for (3x3)(5x2)
15x5
Simplify: (3r7)4
The entire term 3r7 is raised to the 4th power, so we have 3r7 x 3r7 x 3r7 x 3r7 =
so, we have to do 3x3x3x3 and (r7)4 which gives us 81x28
Write an expression equivalent to (fg2h3)4
f4g8h12
Enter the value of n that makes the expression (y2 x z0)3= yn true.
n=6
Write an expression equivalent to v-8 / v-5.
v-3 or 1 / v3
What is the value of m that makes this expression true?
713 = 7m x 75
m = 8
Simplify the expression: (5-2)2
5-4
Apply the properties of exponents to simplify the following expression:
(4xy)(5x5y7)
20x6y8
Solve: (50)3
(50)3 = 50x3 = 50 = 1
Write 1 / x9 as a base with a negative exponent.
x-9