# Lesson 4

Dividing Powers of 10

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

### Problem 1

Evaluate:

- \(10^0\)
- \(\frac{10^3}{10^3}\)
- \(10^2 + 10^1 + 10^0\)

### Problem 2

Write each expression as a single power of 10.

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

### 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.)

1 in to 1 mi

1 cm to 1 km

1 in to 10 mi

1 ft to 100 mi

1 cm to 200 km

1 in to 100 mi

1 cm to 1000 km

### Problem 5

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

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

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

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

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

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

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

### 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.

- Write an equation relating the two variables.
- Rearrange the equation so \(b\) is the independent variable.
- Rearrange the equation so \(g\) is the independent variable.

### 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.