Lesson 6.5 • Looking Back with Exponents
Name Period Date
1. Eliminate factors equivalent to 1 and rewrite the right side of this equation.
p p 3 q q 3 5 r r 2 2
2. Use the properties of exponents to rewrite each expression.
a. m m 1 4 0 b. n n 8 c. 2 8 4 x x 5 9
d. 3 4 6 x x y 5y 3
6 e. 45 9 m m 7 4 n n 4 2 f. 5 2 0 x x 1 1 1 2 y y 6 8
g. 42 6 x x 1 3 0 y y5 h. 1 3 2 m m 4 5 n n 2 7 i. 5 1 r 5 4 r s 1 2 2s5
3. Lana bought a car 8 years ago.Since she purchased it,the value of the car has decreased by 12% each year.The car is now worth about
$5900. a. Which letter in the equation y A(1 r)x could represent the value of the car 8 years ago when Lana bought it? b.
Substitute the other given information into the equation y A(1 r)x. c. Solve your equation in 3b to find the value of Lana’s car
when she bought it.
4. Use the properties of exponents to rewrite each expression. a. (3x)22×24 b. 4 4 y y 2 2 6 5 c. ( 4 2 z z 2 )
2 3 d. 3a2b2(2ab)3
e. 4 1 . . 2 2
1 1
0 0 9 5 f. 5r3 2 s 0 6 r 4 4 s8 rs22
5. a. In 2004Canadahadapopulationof about3.25 107 people.Canada hasanareaof approximately3.51 106 squaremiles.Findthe
populationdensityof Canada(thenumberof peoplepersquaremile). b. In 2004 the United States had a population of about 2.93 108
people.The United States has an area of approximately 3.54 106 square miles.Find the population density of the United States. c. How
did the population densities of Canada and the United States in 2004 compare?
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