Name: 9.2 9.2 Rational Exponents A. n a A radical can be written as a ____________________________________. In general,_____________________________. EX 1: Express as a radical expression and simplify. 1
2
1
3
1
1
6
b. (4x ) 2 a. 64 d. 15x 3 3
c. (−27x ) m
B. a When you have an exponent in your radical you write it as:_________________________________. EX 1: Rewrite using radical notation and simplify. n
2
3
3
a. (−8x ) b. 3x
2
5
2
c. (64x 3 ) 3
C. a − n To convert a negative exponent in the numerator to a ________________ exponent, write over ____. For example, ___________________. EX 1: Simplify. m
− 14
a. −81
6 −4 3
b. (27a )
⎛ y8 ⎞
c. ⎜⎝ 16 ⎟⎠
−1
−3
2
d. (−8x ) vs. −8x
2
2
−3
2
Maya Lanzetta MAT 122 Math is radical! ~Bumper Sticker E. Laws of Exponents Negative Exponent Rule Quotient Rule Product Rule Power Rule Distribute Powers EX 1: Use the laws of exponents to simplify. a. 9 ⋅ 9 2 b. 4x 5 ⋅ x 5 EX 2: The number of Earth days it takes a planet in the solar system to revolve around the Sun can be approximated by 1
1
3
2
the expression 0.4(D 2 ) , where D is the average distance of the planet from the Sun in millions of miles. a. Write this expression in radical form. b. The planet Mercury is an average distance of 36 million miles from the Sun. To the nearest day, how many Earth days does it take Mercury to revolve once around the Sun? EX 3: 3
4096 Challenge: 5
2