Smart Notes
Unit 4 ­ Day 2
Defining Integral & Rational Exponents
Learning objective­ determine, through investigation using technology, that the equation of a given exponential function can be expressed using different bases [e.g., f
﴾x﴿ = 9 can be expressed as f﴾x﴿ =3 ], and explain the connections between the equivalent forms in a variety of ways ﴾e.g., comparing graphs; using transformations; using the exponent laws﴿.
Defining Integral & Rational Exponents
You may recall that "Integers" are positive and negative whole numbers. This leads us directly to the definition of Integral Exponents.
Integral Exponents
ie.
These are exponents which are positive or negative whole numbers.
7 ­ 2 or ( ­ 4 ) ­ 3
To evaluate an Integral Exponent use:
a ­ b = 1 b
a
Note that an exponent of Zero is considered Integral. So..
a 0 = 1
You may recall that "Rational Numbers" are numbers that may be written in fractional form. This leads us to the definition of Rational Exponents.
Rational Exponents
"Rational Exponents" are exponents written in a fractional form.
ie. 5 ¼ or
21 ¾
To evaluate "Rational Exponents" we use Roots.
1 a
a
a = √a
Examples:
a) 125
1 3
Evaluate each of the following using Exponent Rules.
2 5
b) 243
3 c) 36 2
Example:
5 2
a) ( )
7
Evaluate each of the following using exponent rules.
b) 125 343
( )
2 3
c) 16 ( )
81
3 4
Example:
Determine the value of the following to 3 decimal places accuracy.
a) 290 1.26
b) 21 ­ 4.6
c) ( ­ 3.4 ) 2.8
Homework:
Ex 1.5 Pg.
# 4 ­ 12