MATH IS FUN!!!. Let’s start by reviewing exponent laws!

MATH IS FUN!!!MATH IS FUN!!!

Let’s start by reviewing Let’s start by reviewing exponent laws!exponent laws!

Multiplying powers …Multiplying powers …

If you are If you are multiplyingmultiplying powers with the same powers with the same base …base …

3344 x 3 x 366

(here both numbers have a base of 3)(here both numbers have a base of 3)Then … you keep the base the same and Then … you keep the base the same and ADDADD the the

exponentsexponents

3344 x 3 x 366 = 3 = 3 (4 + 6)(4 + 6)

= 3= 31010

Try These…Try These…(Do them on a sheet with your name and the (Do them on a sheet with your name and the

date – they will be collected next class!)date – they will be collected next class!)

Simplify.Simplify.

1.1. (3(322)(3)(344))

2.2. (4(433)(4)(477)(4)(422))

3.3. (5(533)(5))(5)

Dividing powers …Dividing powers …

If you are If you are dividingdividing powers with the same powers with the same base …base …

7755

7733

Then … you keep the base the same and Then … you keep the base the same and you you SUBTRACTSUBTRACT the exponents the exponents

7755 ٪٪ 7733 = 7 = 7 (5 - 3)(5 - 3)

= 7= 722

Do these on your page …Do these on your page …

Simplify.Simplify.

1.1. 2255 2222

2. 2. 10101010

101088

3. 3. kk44

kk

Exponents of exponents …Exponents of exponents …

If you have to If you have to simplifysimplify a power of a power a power of a power with the same base …with the same base …

(2(255))33

Then … keep the base the same and Then … keep the base the same and MULTIPLYMULTIPLY the exponents the exponents

(2(255))33 = 2 = 25x35x3

= 2= 21515


Express as a single power.Express as a single power.

1.1. (10(1033))22

2.2. (28(281313))00

3.3. (6(6-1-1))-1-1

Sometimes exponents of Sometimes exponents of exponents can get tricky!!exponents can get tricky!!

What happens when there are What happens when there are variables in the question?variables in the question?

((xx22yy33)(x)(x44yy22))

This expression can also be written as This expression can also be written as

xx22 xx y y33 xx x x44 x x yy2 2 = (x = (x22 xx x x44) ) xx (y (y33 xx y y22))

And we know that when we And we know that when we multiplymultiply powers powers with the same base, we with the same base, we ADDADD the the

exponents, so …exponents, so …(x(x22 xx x x44) ) xx (y (y33 xx y y22) = (x ) = (x 2 + 42 + 4)(y )(y 3 + 23 + 2))

= x= x66yy55


Simplify.Simplify.

1.1. (w(w-6-6)(w)(w-7-7))

2.2. (x(x44))22

3.3. hh-8-8

hh-9-9

((xx22yy33))33

In this case, the 3 outside the bracket must apply In this case, the 3 outside the bracket must apply to to EVERYTHINGEVERYTHING inside the bracket! inside the bracket!

((xx22yy33))33 = (x = (x22yy33)(x)(x22yy33)(x)(x22yy33))

This is just like the last example!This is just like the last example!OROR

We know that when we want to We know that when we want to simplifysimplify the power the power of a power, we of a power, we MULTIPLYMULTIPLY the exponents the exponents

((xx22yy33))3 3 = (x = (x2x32x3)(y)(y3x33x3)) = x= x66yy99


Simplify.Simplify.

1.1. (x(x55yy22))33

2. (mp)2. (mp)44(m(m55p)p)

3. (t3. (t33ww99)(t)(t22))55

But what if there are numbers and But what if there are numbers and variables???variables???

(-x(-x22))100100

The exponent must still be applied to The exponent must still be applied to EVERYTHINGEVERYTHING inside inside the bracket!the bracket!

(-x(-x22))100 100 is the same asis the same as (- (-11xx22))100100

In this case, the 100 applies to the -1 AND the xIn this case, the 100 applies to the -1 AND the x22

(-(-11xx22))100 100 = (-= (-11))100100(x(x22))100100

= 1= 1xx 2x1002x100

= 1x= 1x200200


Simplify.Simplify.

1.1. (-10y(-10y55))44

2.2. (3m(3m22))22

3.3. (5h(5h55mm33))9 9 remember the 9 applies to remember the 9 applies to everything in the brackets … (the everything in the brackets … (the 5, the h5, the h55 and the m and the m33))

Ok, now for something a little bit Ok, now for something a little bit new!!!new!!!

You know how to simplify expressions with You know how to simplify expressions with exponents, but sometimes you are asked exponents, but sometimes you are asked to evaluate them after they are simplified.to evaluate them after they are simplified.

BUTBUT … what do you do with a … what do you do with a negative negative exponentexponent?!??!?

(3(3-2-2)(3)(3-1-1))

We know that when we We know that when we multiplymultiply powers with powers with the same base, we the same base, we ADDADD the exponents … the exponents …

(3(3-2-2)(3)(3-1-1) = 3) = 3(-2 + -1)(-2 + -1)

= 3= 3-3-3

How do we evaluate this??How do we evaluate this??

33-3-3

Anytime you have a negative exponent, you Anytime you have a negative exponent, you can make it into a positive exponent by can make it into a positive exponent by

putting a 1 over number!putting a 1 over number!

33-3-3 = = 113333

= = 1199

Let’s see another one of those …Let’s see another one of those …

If we have the following:If we have the following:

55-7-7 remember we remember we SUBTRACTSUBTRACT the the 55-3-3 exponents exponents

55-7-7 = 5 = 5(-7 - -3) (-7 - -3) = 5= 5-4-4

55-3-3

Now, we simply put 5Now, we simply put 5-4-4 under a 1 under a 1 1_1_ 554 4 (it becomes positive)(it becomes positive)

And we can evaluate it as we would any positive exponent …And we can evaluate it as we would any positive exponent …

11 = = 115544 625 625


From page 230 in your textbook:From page 230 in your textbook:

Questions 9, 10 and 11(a, c, e)Questions 9, 10 and 11(a, c, e)

Remember I will be collecting this work next class! Remember I will be collecting this work next class! If you have difficulty, review the slides and then If you have difficulty, review the slides and then

ask one of your classmates to help you!ask one of your classmates to help you!

Jorge – try it on your own first!!!Jorge – try it on your own first!!!

HAVE A GREAT DAY!!!HAVE A GREAT DAY!!!

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MATH IS FUN!!!. Let’s start by reviewing exponent laws!