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Published on March 9, 2014

Author: vincentthato

Source: slideshare.net

Exponents VINCENT LEPING 08/03/2014

For Learning to Happen! •Clear your desk of anything that may distract you. •Remove all other thoughts from your mind. •Pay close attention. •Try all the examples. •Ignore all other distractions.

Definition of Exponent  An exponent tells how many times a number is multiplied by itself. Base 3 4 Exponent

Review: What do exponents tell us? 3 What does 5 mean? 3 =5 5 5 5

What is the “base”? What is the “exponent”? 8 5

What an Exponent Represents  An exponent tells how many times a number is multiplied by itself. 4 3 =3x3x3x3

3 6 Write in standard form. 3 6 =6 6 6 = 216

4 6 Write in standard form. 4 = 6 6 6 6 6 = 1,296

What happens if we multiply 3 6 4? 6 3 6 4= 6 (6 6 6) (6 6 6 6)

So… 3 4= 67 because we 6 6 used 6 as a factor seven times! Notice anything?

Let’s try another example: What is 2 5 4= 5 or 2 5 (5 4= 5 2 5 5) 6 5 4? 5 (5 5 5 5)

For MULTIPLICATION: x s x =x t s+t (For any number x and for integers s and t.)

In other words, when multiplying two numbers in exponential form with the same base, add the exponents.

Ex: 4 9 9 =? 8 9 12

What happens if we divide? 75 73 75 = 7 7 7 7 73 7 7 7 7 Cancel out any numbers that are in the numerator AND denominator!

After we cancel, we are left with 72. So, 75 = 72 3 7

For DIVISION: s x t x = x s-t (For any nonzero number x and for integers s and t.)

In other words, when dividing two numbers in exponential form with the same base, subtract the exponents.

Ex: 8 6 6 5= 6 3 ?

What about 2)3? (5 2)3 (5 2) (5 (5 6 5 2) (5 5) (5 2) (5 5) (5 5)

Raising a power to a power: s)t (x =x s t (For any number x and for integers s and t.)

In other words, when raising a number with an exponent to a power, multiply the exponents.

Ex: 3) 7 = ? (5 21 5

One important thing to remember… 0 = 1 x (Any number to the zero power is equal to 1!)

Why??? For 2 3 example… 2 3 =3 2-2 3 3 =9 =1 = 2 3 3 3 9 2 3 = 0 3

So, 0= 3 1 This works for any base number!

Can we have negative exponents?  Yes! Negative exponents represent the reciprocal. 1  The reciprocal of x is x The reciprocal of 10 is  They 1 10 do NOT make the answer negative.

1 1 -2 5 = 2= 25 5 1 2 = 4 2 -4 1 16

REFERENCE LIST  Melnichenko, Y. (2008, September 14). Exponents. Retrieved March 08, 2014, from http://www.slideshare.net/yelena585/exponentspresentation  Yuskaitis, M. (2008, June 06). Exponents. Retrieved March 08, 2014, from http://www.slideshare.net/hiratufail/exponents1

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