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6-8 Accelerated 7 Unit 7 Lesson 6

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 •Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 7, Lesson 6

Practice with Rational Bases

Accelerated 7

Practice

Problem 1

Write with a single exponent:

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

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Lesson 6 Resources

Student Materials

Problem 2

Determine whether each of the following equations is true or false? Explain or show your reasoning.

\((7^2)^3 = 7^5\)
\(2^4 \boldcdot 2 = 2^5\)
\(2^2 \boldcdot 3^4 = 6^6\)
\(( (\frac23)^2 )^4 = (\frac23)^8\)

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Problem 3

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.

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Problem 4

ForLesson 15: Solving Systems of Equations

Lin says that the system of equations \(2x + 6y = 10\) and \(3x + 9y = 15\) has an infinite number of solutions.

Do you agree with Lin? Explain your reasoning.
Write a new equation that makes a system with infinite solutions together with \(2x + 6y = 10\).
Describe the graph of the new system.

to access Practice Problem Solutions.