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?
![A scatterplot. Horizontal, from 1980 to 2020, by 10’s. Vertical, from 90 to 115, by 5’s. 14 data points trend slightly linearly downward and right.](https://cms-im.s3.amazonaws.com/UqPz2aM5XqX6E2dyP9Lu3Xcu?response-content-disposition=inline%3B%20filename%3D%228-8.6.PP.B.Image.31.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.PP.B.Image.31.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T235955Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4cf559aa75ec85d94560bad28422e354a349ec643e936f21a81a5e90463a7fa1)
The slope is positive.
The slope is zero.
The slope is negative.
There is no association.
Solution
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(From Unit 5, Lesson 21.)