Open Up - Grade 8 - Mathematics - Unit 7 - Lesson 8

Select all the true statements:

Find x, y, and z if (3⋅5)^{4}⋅(2⋅3)^{5}⋅(2⋅5)^{7}=2^{x}⋅3^{y}⋅5^{z}

Han found a way to compute complicated expressions more easily. Since 2⋅5=10, he looks for pairings of 2s and 5s that he knows equal 10. For example, 3⋅2^{4}⋅5^{5}=3⋅2^{4}⋅5^{4}⋅5=(3⋅5)⋅(2⋅5)^{4}=15⋅10^{4}=150,00. Use Han's technique to compute the following:

2^{4}⋅5⋅(3⋅5)^{3}

Han found a way to compute complicated expressions more easily. Since 2⋅5=10, he looks for pairings of 2s and 5s that he knows equal 10. For example, 3⋅2^{4}⋅5^{5}=3⋅2^{4}⋅5^{4}⋅5=(3⋅5)⋅(2⋅5)^{4}=15⋅10^{4}=150,00. Use Han's technique to compute the following:

\frac{2^{3}⋅5^{2}⋅(2⋅3)^{2}⋅(3⋅5)^{2}}{3^{2}}

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 dollars per pound.

• Store B sells the same cheese for 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 dollar per pound, but with a $10 delivery fee.

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

Match Stores A, B, and C with Graphs