Math 10

4.3 Rational Exponents

Recall the exponent laws:

Multiplying powers with the same base (am )(an) = am+n

Dividing powers with the same base am rn-n= aan

A Power Raised to a Power (amt = am"n

Power of a Quotient u. n an=b bn

Power of a Product (ab)" = an'bn

Zero Exponent aO= 1

We use these SAME laws when working with RATIONAL EXPONENTS.

What is a rational number?

- A number that can be expressed as a fraction (~ ) where a and bare

integers; and b is not equal to zero, • t::: .5. 5e~..__:...J) ) ---- I' >

\ 8- -=rIntegers

- ~.\-/l 0 ~i" 1,+2..i:::- ~ .,.

Rational Numbers:

(all integers, repeating decimals,terminating decimalsl ~ repe«-f)~.~) /.,Jj .) L

Irrational Numbers

A power with a rational exponent can be written as:~-;)...., ~ O.~

.s. .. L1

, Lr )~ \+rCLL-\-)on d~l;!Y\t\ \

x

\- '1

r Ilor~ ---

Quick Review of Operations with Fractions:

Multiplying fractions: . <..)1.. ~ 3e:« ~ ~ Y- -z: --

5-4 '>0"j..

Dividing fractions: (multiply by reciprocal)

" ------------

(find common denominator)

doe-s no\ 9 e:-\ ~J,

9 - \4® \~

''N~\f\) orvrUS0

-fD '( exfl\ ttw S . Adding and Subtracting fractions:

Ct)\Y\ yY\O\l def I ~ac

~

+hc\'~ WLtf\ l(}.A V\V,( Gt~

'f7X.poy\.(n\:S .More Examples of Rational Exponentsrz-. 1-\ Ou5 3'1-0.5

(4X3rv= 1" X

Decimal Fraction0.25 \--

\ . ~~\ 0.5 -L

d-0.75 3---q=-1.5 .z,

o:

Going Between Decimals and Fractions

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Word Problem:

The bacterium Lactobacillus bulgaricus is used to make yoghurt and cheese. Thegrowth of 10 000 bacteria can be modeled by the formula:

r""ou~ .N = 10000 (2)h/42

, I

5' Cty-\- ~I'\ hWhere N is the number of bacteria after h hours.

a) What does the value 2 in the formula tell you?

::l --k\\s ~OlA ~L ba.L-KnOc oI.CMbk.J Clt'--Ur-L\-'~ "'0\,\ (S.

b) How many bacteria are present after 42 hours?

N -:: \ (J 000 ('J. ')~;}...\

-\ 0 000 ( ~ ')N ~\ ~o aDO]

c) How many bacteria are present after 105 hours?

'~()j DOO blle,.\e.( ~o: ~~r42- n~'

N ~ \0 600 (~)~ta 5

<:: \0 bOO (2-) .

co.\tM~· [=- \0 000 ill J. IE1 ~. 5]

~ \}565 b8 · S l\- 1b(k-\t~Ct a:.\'4u" 4:l- hrs

Do 4.2 Questions: Rational Exponents

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