# Lesson 7

Practice with Rational Bases

Let's practice with exponents.

### Problem 1

Write with a single exponent:

1. $$\frac{7^6}{7^2}$$
2. $$(11^4)^5$$
3. $$4^2 \boldcdot 4^6$$
4. $$6 \boldcdot 6^8$$
5. $$(12^2)^7$$
6. $$\frac{3^{10}}{3}$$
7. $$(0.173)^9 \boldcdot (0.173)^2$$
8. $$\frac{0.87^5}{0.87^3}$$
9. $$\frac{(\frac{5}{2})^8}{(\frac{5}{2})^6}$$

### Problem 2

Noah says that $$2^4 \boldcdot 3^2 = 6^6$$. Tyler says that $$2^4 \boldcdot 4^2 = 16^2$$.

1. Do you agree with Noah? Explain or show your reasoning.
2. Do you agree with Tyler? Explain or show your reasoning.

### Problem 3

Make a sketch of a linear relationship with a slope of 4 and a negative $$y$$-intercept. Show how you know the slope is 4 and write an equation for the line.

(From Unit 5, Lesson 7.)

### Problem 4

Using the data in the scatter plot, what can you tell about the slope of a good model?

A:

The slope is positive.

B:

The slope is zero.

C:

The slope is negative.

D:

There is no association.

(From Unit 5, Lesson 21.)