Lesson 1

Properties of Exponents

Problem 1

Find the value of each variable that makes the equation true.

  1. \(2^5 \boldcdot 2^3 = 2^a\)
  2. \(\frac{7^4}{7^b} = 7^{\text- 2}\)
  3. \(8^c = \frac{1}{64}\)

Solution

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Problem 2

Select all the expressions equivalent to \(7^{\text- 2} \boldcdot 7^5 \boldcdot 7^{\text- 3}\).

A:

\(0\)

B:

\(1\)

C:

\(\frac17\)

D:

\(7^0\)

E:

\(7^{10}\)

Solution

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Problem 3

Which expression is equal to \(\frac{3^8}{3^2}\)?

A:

\(1^6\)

B:

\(3^{\text- 6}\)

C:

\(3^4\)

D:

\(3^6\)

Solution

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Problem 4

Find the value of each variable that makes the equation true.

  1. \(\frac{5^6}{5^m} = 5^9\)
  2. \(2^3 \boldcdot 4^n = 2^{11}\)
  3. \((7^4)^k = 7^{\text-8}\)

Solution

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Problem 5

  1. Evaluate the expression \(\frac{6^3}{6^3}\).
  2. Explain how this helps show why \(6^0 = 1\).

Solution

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