Lesson 8: Practice Problems

Problem 1

Select all the true statements:

$2^{8} \cdot 2^{9} = 2^{17}$
$8^{2} \cdot 9^{2} = 72^{2}$
$8^{2} \cdot 9^{2} = 72^{4}$
$2^{8} \cdot 2^{9} = 4^{17}$

Problem 2

Find $x$ , $y$ , and $z$ if ${(3 \cdot 5)}^{4} \cdot {(2 \cdot 3)}^{5} \cdot {(2 \cdot 5)}^{7} = 2^{x} \cdot 3^{y} \cdot 5^{z}$ .

Problem 3

Han found a way to compute complicated expressions more easily. Since $2 \cdot 5 = 10$ , he looks for pairings of 2s and 5s that he knows equal 10. For example, $3 \cdot 2^{4} \cdot 5^{5} = 3 \cdot 2^{4} \cdot 5^{4} \cdot 5 = (3 \cdot 5) \cdot {(2 \cdot 5)}^{4} = 15 \cdot 10^{4} = 150, 000.$ Use Han’s technique to compute the following:

$2^{4} \cdot 5 \cdot {(3 \cdot 5)}^{3}$
$\frac{2^{3} \cdot 5^{2} \cdot {(2 \cdot 3)}^{2} \cdot {(3 \cdot 5)}^{2}}{3^{2}}$

Problem 4 From Unit 6 Lesson 8

The cost of cheese at three stores is a function of the weight of the cheese. The cheese is not prepackaged, so a customer can buy any amount of cheese.

Store A sells the cheese for $a$ dollars per pound.
Store B sells the same cheese for $b$ dollars per pound and a customer has a coupon for $5 off the total purchase at that store.
Store C is an online store, selling the same cheese at $c$ dollar per pound, but with a $10 delivery fee.

This graph shows the price functions for stores A, B, and C.

A graph with lines j, k, and l of weight of cheese in pounds vs cost in dollars. Line J points: (0,10) and 7,30). Line K points: (1,0) and (5,20). Link L points: (0,0) and (5,20).

Match Stores A, B, and C with Graphs $j$ , $k$ , and $ℓ$ .
1. Store A
2. Store B
3. Store C
1. Graph $j$
2. Graph $k$
3. Graph $ℓ$
How much does each store charge for the cheese per pound?
How many pounds of cheese does the coupon for Store B pay for?
Which store has the lowest price for a half a pound of cheese?
If a customer wants to buy 5 pounds of cheese for a party, which store has the lowest price?
How many pounds would a customer need to order to make Store C a good option?