Simplifying Powers 2023
Powers
Notice:  You must multiply the coefficients (#s in frontof the powers).
-3am •2an = -6am+n
Multiplying Powers
am •an = am+n
Simplify the following problems COMPLETELY!
Before you begin, remember...
(Don't pick any answer with these exponents!)
You cannot leave your final answer with any zero or negative exponents!
You should not see the same variable more than once.
To multiply powers with the same base,
Pick:  add, subtract, multiply, or divide
you must write the base and
the exponents
x2
x3
x4
.
.
.
x-1 = x
x-3 = x
x5
= x
=
2n
.
4n = 
6n
6n2
8n
8n2
15y6
8y6
5y
.
3y6 = 
15y7
8y7
Drag the correct answers to the blocks.
3t4
-3t2
3t3
-3t4
.
.
.
.
-2t2  =
2t-2 =
-2t-2 =
2t = 
-6t6 
?
-6t5
?
-6t  
?
-6   
?
9x2 • 2x-2
18x
18
18
18x-4
x4
-3t3 • -2t
6t4
-5t4
6t3
5t3
7n6(3n5)
10n30
21n30
10n11
21n11
-5z3• 7z4
-35z7
-35z12
35z12
2z7
2xy• x6y2
2x6y6
2x7y6
2x6y8
2x7y8
4a0• 5a3•-2a5
-40
-40a9
-20a8
-40a8
-4k2 • 7k-1
-28
k
28
k2
-28k
1
28k
6mn-4 • m5n2
6m5n-2
6m6n2
6m5
6m6
n2
n2
a-3b2 • a-4b-1
a12b
a-7b
a12
b
a7
b2
-b3c • 5b-4c
5c
-5c2
b7
b
-5c2
c2
5b
b7
9m4n-3p • -m2n3p-5
-9m6n
m6n0
9p4
p4
-9m8
-9m6
p5
p4
Simplify
3-3
1/27
1/9
-1/27
-27
Simplify
x-2
1/x2
-x2
-1/x2
x2
Simplify
50
0
1
5
1/5
Simplify
-40
-4
4
1
-1
Simplify
(-2)0
1
-1
2
-2
Simplify
m-5
m5
-m5
1/m5
-1/m5
Simplify
4t-3
-1/4t3
-4t3
1/4t3
4/t3
Simplify
(3m)-2
3/m2
9/m2
1/9m2
-1/9m2
Simplify
(5k)0
1
5k
5
1/5k
(Power)
(am)n = amn
Raising Powers to Powers
Power

(write the base,
multiply the exponents)
Simplify.
Make sure you have no zero or negative
exponents in your answers!
Don't forget to raise your coefficients to the power, too!Ex:  (2m3)3 = 23 • (m3)3
= 8m9
When raising a power to a power,
__________the exponents
  add
  multiply
  subtract
  divide
you must
(x2)3
x6
x5
x8
x1

(3t5)3
9t15
27t15
3t15
27t8
(b-2)-5
b-7
b-10
b7
b10
(5w-2)2
25w-4
25
w4
5w4
    1
25w4
Remember:  x = x1
Dividing Powers
Simplify each problem completely!
(no zero or negative exponents!)
(variable does not appear twice!)
(Subtract the exponents!)
(with the same base)
Make sure you divide the
coefficients!
am
an
= a(m-n)
m-1
m2
x3
x
= m
= x
g
g-4
g3
g-3
g5
1
g5
a3b2
a5b2
a2b4
a15b4
a2b0
a2
x6y7
x2y
 1
 x4
x4y6
y6
x12y7
 1
x4y7
  m
  1
 m9
m5
m-4
  m9
  1
m
25xy3
  20y4
  5
5xy-1
y2
  5xy4
  5y4
The voice inside
your head that says
that you can't do this,
is a 
    
LIAR!
-9a-1b4
 -3
  3
3ab-4
  -3b8
  -3
a2b8
a2
8m5n2
  n
4m2n
  2  
m3n2
4m3
  1
  1
2m3n
2m3
simplify:
7mp2
mp2
7n6
n3
21mn2p-1
3m2n-4p
m3p2
7m
n2p2
7n6
4x8y-5
20x3
5x5y-2
x5
x5
x11y8
5y8
5x2
5
Solve:  
32x - 2 = 35x + 7
x = 
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