# Lesson 7

Practice with Rational Bases

### Problem 1

Write with a single exponent:

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

### Solution

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### Problem 2

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

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

### Solution

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### 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.

### Solution

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(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?

The slope is positive.

The slope is zero.

The slope is negative.

There is no association.