Lesson 7
Practice with Rational Bases
Let's practice with exponents.
Problem 1
Write with a single exponent:
- \(\frac{7^6}{7^2}\)
- \((11^4)^5\)
- \(4^2 \boldcdot 4^6\)
- \(6 \boldcdot 6^8\)
- \((12^2)^7\)
- \(\frac{3^{10}}{3}\)
- \((0.173)^9 \boldcdot (0.173)^2\)
- \(\frac{0.87^5}{0.87^3}\)
- \(\frac{(\frac{5}{2})^8}{(\frac{5}{2})^6}\)
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.
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.
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T074028Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c910d5608a74531e3b930b28dee18c6e62624b42f380fe24ae83aeeb9d6fd36c)
A:
The slope is positive.
B:
The slope is zero.
C:
The slope is negative.
D:
(From Unit 5, Lesson 21.)
There is no association.