Lesson 7

Practice with Rational Bases

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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. \(\frac{(\frac{5}{2})^8}{(\frac{5}{2})^6}\)

Solution

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Problem 2

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

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

The slope is positive.

B:

The slope is zero.

C:

The slope is negative.

D:

There is no association.

Solution

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(From Unit 5, Lesson 21.)