Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!

7 4 7 is the base 4 is the exponent The base is used as a factor 4 times.

Expanded notation: 5 x 5 x 5 x 5 x 5 x 5 Exponential notation: 5 6 Evaluated Notation: 15,625

-5 4 = ? (-5) 4 = ? Are they the same? Explain = ? (-2) 4 = ? Evaluate both.

(-5) 4 Will this value be negative or positive? (-5) 3 Will this value be negative or positive? Explain.

3 2 x 3 5 Means 3 x 3 x 3 x 3 x 3 x 3 x 3 Can you see a short cut? Try it! 5 4 x 5 6 = ? 2 7 x 2 6 =?

7 2 x x 7 x 7 x 7 x 7 x 7 x 7 Or7 823,543

We can do this with variables also! w 3 w 2 w x w x w x w x w w 5

(2a 2 ) (3a 5 ) Apply the commutative property to re- arrange the elements of the expression. 2 x 3 x a 2 x a 5 6a 7

Power of a Power (6 3 ) 4 Means this: 6 3∙ 6 3 ∙6 3 ∙6 3 Or 6 12

(4 5 ) x (52)4(52)4 52 x 52 x 52 x 5252 x 52 x 52 x

What about this? =

Therefore anything to the zero power equals 1.

Negative Exponents! 5 -3 = ab -2 = a b = = =

SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.

Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers.

Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 10 5 is not in proper scientific notation. Why?

Soooo 137,000,000 can be rewritten as 1.37 X 10 8

Now You Try Using scientific notation, rewrite the following numbers. 347, X ,000, X , X 10 4

Convert these: 1.23 X , X ,806,000

Try These 4,000 4 X X , X ,123, ,000, X 10 8

In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation. 1.5 X 10 7

The U.S. has a total of X 10 7 acres of land reserved for state parks. Write this in standard form. 12,916,000 acres

Why does a Negative Exponent give us a small number? = 10 x 10 x 10 x 10 = = 10 x 10 x 10 = = 10 x 10 = = = 10 0 Do you see a pattern?

Sooooo = = = = = = = 10 -4

Your Turn Using Scientific Notation, rewrite the following numbers X X X 10 -5

Change to Standard Notation 3.89 x x x ,250,000

More Examples 1) X ) X ) X ) X ) X 10 -4

The nucleus of a human skin cell is about 7 X meters in diameter. What is the length in standard notation?

A ribosome, another part of a cell, is about of a meter in diameter. Write the length in scientific notation. 3 X 10 -9

Metric System Napoleon- to unite his empire Used everywhere except U.S. Based the number 10 Basic unit of length: meter Basic unit weight: gram Basic unit volume: liter

kilo hecto deka unit (meter or liter or gram) deci centi milli To go down you multiply by ten for each step. To go up you divide by ten for each step.