EXPONENTS

• Definition• Negative Exponents• Multiplication of Exponents• Dividing Exponents• Raising Exponents• Add & subtract Exponents• Base of 10 rule• Scientific Notation

WHAT ARE EXPONENTS? Exponents are equations where a base number is multiplied by itself a

number of times designated by the superscript also known as power or index.

𝑎3 Base

Power

=

MATC- TOPIC 1- Exponents

LETS TRY IT!! 24

1. Identify the base

2. Identify the power

2

4

3. Write out the problem 2x2x2x2

4. Solve the problem 16

MATC- TOPIC 1- Exponents

NEGATIVE EXPONENTS Negative exponents = reciprocal of the base

Reciprocal is the number in the form

x x

MATC- TOPIC 1- Exponents

LETS TRY IT!!

2− 4

x x2− 4 =

MATC- TOPIC 1- Exponents

MULTIPLYING AND DIVIDING EXPONENTS Multiplying exponents = adding exponents (superscript)numbers

x =

Dividing exponents = subtracting exponents (superscript) numbers

=

MATC- TOPIC 1- Exponents

LETS TRY IT!!

x 24+5

292 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2512MATC- TOPIC 1- Exponents

LETS TRY IT!!

25− 4

212 MATC- TOPIC 1- Exponents

EXPONENT TO THE “N” POWER When raising an exponent to a high power (n) this requires

multiplication of exponents.

n =

MATC- TOPIC 1- Exponents

LETS TRY IT!! 21×3232 x 2 x2 8

MATC- TOPIC 1- Exponents

NOW WHAT HAPPENS IF I OPEN UP A CAN OF WORMS AND HAVE YOU PERFORM THE PREVIOUS EXPONENT LESSONS WITH MULTIPLE BASES?

MATC- TOPIC 1- Exponents

MANIPULATING EXPONENTS WITH DIFFERENT BASES

1. Expand each base and its corresponding exponent.2. Add, subtract, multiply or divide the two numbers.

+

(4 x 4 x4) + (2 x 2 x 2)64 + 8

72Step 1

Step 2

MATC- TOPIC 1- Exponents

POWER OF ZERO? Law of exponents states any base raised to the power of zero is

equal to 1

∞ 0=1

MATC- TOPIC 1- Exponents

EXPONENTS WITH BASE OF 101. If the exponent is greater than 1 (positive) then the zeros will be after the base number

Ex) = 1,000,000

2. If the base number is less than 1 (negative) then the zeros will be to the right of the decimal point

Ex) = 0.000001

MATC- TOPIC 1- Exponents

SCIENTIFIC NOTATION By using the law of exponents with base of 10 we can simplify numbers in

standard notation that are large or small.

0.00000000000000000000602 = 6.02 x

Scientific Notation will be your best friend in a laboratory setting especially with cell counts.

100,000,000,000 cells/mL is the same as saying 1 x cells/mL

MATC- TOPIC 1- Exponents