MATH IS FUN!!!

Let’s start by reviewing exponent laws!

Multiplying powers … If you are multiplying powers with the same base … 34 x 36 (here both numbers have a base of 3) Then … you keep the base the same and ADD the exponents 34 x 36 = 3 (4 + 6) = 310

Try These… (Do them on a sheet with your name and the date – they will be collected next class!) Simplify. (32)(34) (43)(47)(42) (53)(5)

Then … you keep the base the same and you SUBTRACT the exponents Dividing powers … If you are dividing powers with the same base … 75 73 Then … you keep the base the same and you SUBTRACT the exponents 75 ٪ 73 = 7 (5 - 3) = 72

Do these on your page … Simplify. 25 22 2. 1010 108 3. k4 k

Exponents of exponents … If you have to simplify a power of a power with the same base … (25)3 Then … keep the base the same and MULTIPLY the exponents (25)3 = 25x3 = 215

Do these on your page … Express as a single power. (103)2 (2813)0 (6-1)-1

Sometimes exponents of exponents can get tricky!! What happens when there are variables in the question?

(x2y3)(x4y2) This expression can also be written as x2 x y3 x x4 x y2 = (x2 x x4) x (y3 x y2) And we know that when we multiply powers with the same base, we ADD the exponents, so … (x2 x x4) x (y3 x y2) = (x 2 + 4)(y 3 + 2) = x6y5

Do these on your page … Simplify. (w-6)(w-7) (x4)2 h-8 h-9

This is just like the last example! (x2y3)3 In this case, the 3 outside the bracket must apply to EVERYTHING inside the bracket! (x2y3)3 = (x2y3)(x2y3)(x2y3) This is just like the last example! OR We know that when we want to simplify the power of a power, we MULTIPLY the exponents (x2y3)3 = (x2x3)(y3x3) = x6y9

Do these on your page … Simplify. (x5y2)3 2. (mp)4(m5p) 3. (t3w9)(t2)5

But what if there are numbers and variables??? (-x2)100 The exponent must still be applied to EVERYTHING inside the bracket! (-x2)100 is the same as (-1x2)100 In this case, the 100 applies to the -1 AND the x2 (-1x2)100 = (-1)100(x2)100 = 1x 2x100 = 1x200

Do these on your page … Simplify. (-10y5)4 (3m2)2 (5h5m3)9  remember the 9 applies to everything in the brackets … (the 5, the h5 and the m3)

Ok, now for something a little bit new!!! You know how to simplify expressions with exponents, but sometimes you are asked to evaluate them after they are simplified. BUT … what do you do with a negative exponent?!?

(3-2)(3-1) We know that when we multiply powers with the same base, we ADD the exponents … (3-2)(3-1) = 3(-2 + -1) = 3-3 How do we evaluate this??

3-3 Anytime you have a negative exponent, you can make it into a positive exponent by putting a 1 over number! 3-3 = 1 33 = 1 9

Let’s see another one of those … If we have the following: 5-7  remember we SUBTRACT the 5-3 exponents 5-7 = 5(-7 - -3) = 5-4 5-3 Now, we simply put 5-4 under a 1  1_ 54 (it becomes positive) And we can evaluate it as we would any positive exponent … 1 = 1 54 625

Jorge – try it on your own first!!! Do these on your page … From page 230 in your textbook: Questions 9, 10 and 11(a, c, e) Remember I will be collecting this work next class! If you have difficulty, review the slides and then ask one of your classmates to help you! Jorge – try it on your own first!!!

HAVE A GREAT DAY!!!