# Division Properties of Exponents

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```					Another Multiplication
Property

Module VI, Lesson 3
Online Algebra
VHS@pwcs
Exponents ~ What we have
learned so far!

 Any number to the zero power is 1
 1210 = 1

 When dealing with negative exponents, think of
all numbers/expressions as fractions.
   Then switch all variables taken to negative
exponent to the opposite side of the fraction bar,
making the exponent positive.
   x-5 = 1/x5
 When multiplying powers you add the
exponents.
   x3(x7) = x10
Taking a Power to a Power

(x2)3
 Recall that an exponent tells us how many
times to multiply the base by itself.
 In this problem x2 is the base and 3 is the
exponent, so we multiply x2 by itself 3 times
 x2 * x2 * x2

 Remember to multiply we add the
exponents!
 x2 + 2 + 2 = x6
Taking a Power to a Power

(r5)4
 Recall that an exponent tells us how many
times to multiply the base by itself.
 In this problem r5 is the base and 4 is the
exponent, so we multiply r5 by itself 4 times
 r5 * r5 * r5 * r5

 Remember to multiply we add the
exponents!
 r5 + 5 + 5 + 5 = r20
Taking a Power to a Power

Do you see a pattern yet?
 (x2)3 =   x2 * x2 * x2
= x2 + 2 + 2 = x 6
 (r5)4 = r5 * r5 * r5 * r5
= r5 + 5 + 5 + 5 = r20

Whenever we take a power to a
power, we multiply the exponents!
Try these!

here!
1. (52)5     1. 52*5 = 510
2. (g5)6     2. g5*6 = g30
3. (c-3)-2   3. c-3 * -2 = c6
5 * -3 = b-15 =
1
4. (b5)-3    4. b
b15
Taking a Powers to a Power
(2x2)3
 Recall that an exponent tells us how many times to
multiply the base by itself.
 In this problem 2x2 is the base and 3 is the exponent, so
we multiply 2x2 by itself 3 times
 2x2 * 2x2 * 2x2

 Use the commutative property to rewrite this
expression placing like things together.
   (2 * 2 * 2)(x2 * x2 * x2)
 Multiply (remember to add the exponents)
 8x6
Taking a Powers to a Power
(w3x6)2
 Recall that an exponent tells us how many times to
multiply the base by itself.
 In this problem w3x6 is the base and 2 is the exponent,
so we multiply w3x6 by itself twice.
   w3x6(w3x6)
 Use the commutative property to rewrite this
expression placing like things together.
   (w3 * w3)(x6 * x6)
 Multiply (remember to add the exponents)
 w6x12
Taking a Powers to a Power

 Whenever you take more than one
power to a power, make sure that you
everything in the parentheses is taken to
the power outside the parentheses.

… or in algebra: (ab)n = anbn
Try these!

1. (32d3)4         1. 32*4(d3*4) = 38d12 = 6561d12
2. (-2g5)6         2. (-2)1*6(g5*6) = (-2)6g30 = 64g30
6
3. (bc-3)-2        3. b1*-2 c-3 * -2 = b-2c6 = c
4. (m5n2)-3                                    b2
1
5. (a2b3)8(2a4)3   4. m5 * -3(n2 * -3) = m-15n-6 =
m15 n6

5. a2*8b3*8(23a4*3) = a16b24(8a12)
= 8a28b24
Recap!

Our new exponent properties are:

 Whenever we take a power to a
power, we multiply the exponents.
 Whenever you take more than one
power to a power, make sure that you
everything in the parentheses is taken to
the power outside the parentheses.

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