# Lesson 4

Dividing Powers of 10

Let’s explore patterns with exponents when we divide powers of 10.

### Problem 1

Evaluate:

1. $$10^0$$
2. $$\frac{10^3}{10^3}$$
3. $$10^2 + 10^1 + 10^0$$

### Problem 2

Write each expression as a single power of 10.

1. $$\frac{10^3 \boldcdot 10^4}{10^5}$$
2. $$(10^4) \boldcdot \frac{10^{12}}{10^7}$$
3. $$\left(\frac{10^5}{10^3}\right)^4$$
4. $$\frac{10^4 \boldcdot 10^5 \boldcdot 10^6}{10^3 \boldcdot 10^7}$$
5. $$\frac{(10^5)^2}{(10^2)^3}$$

### Problem 3

The Sun is roughly $$10^2$$ times as wide as Earth. The star KW Sagittarii is roughly $$10^5$$ times as wide as Earth. About how many times as wide as the Sun is KW Sagittarii? Explain how you know.

### Problem 4

Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)

A:

1 in to 1 mi

B:

1 cm to 1 km

C:

1 in to 10 mi

D:

1 ft to 100 mi

E:

1 cm to 200 km

F:

1 in to 100 mi

G:

1 cm to 1000 km

(From Unit 2, Lesson 7.)

### Problem 5

Select all the expressions that are equivalent to $$\text-36x+54y-90$$.

A:

$$\text-9(4x-6y-10)$$

B:

$$\text-18(2x-3y+5)$$

C:

$$\text-6(6x+9y-15)$$

D:

$$18(\text-2x+3y-5)$$

E:

$$\text-2(18x-27y+45)$$

F:

$$2(\text-18x+54y-90)$$

(From Unit 4, Lesson 8.)

### Problem 6

Bananas cost $1.50 per pound, and guavas cost$3.00 per pound. Kiran spends \$12 on fruit for a breakfast his family is hosting. Let $$b$$ be the number of pounds of bananas Kiran buys and $$g$$ be the number of pounds of guavas he buys.

1. Write an equation relating the two variables.
2. Rearrange the equation so $$b$$ is the independent variable.
3. Rearrange the equation so $$g$$ is the independent variable.
(From Unit 6, Lesson 3.)

### Problem 7

Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed $$\frac13$$ of the speed her mom bikes. Sketch a graph of both of these relationships.

(From Unit 5, Lesson 1.)