# Lesson 1

Properties of Exponents

### Problem 1

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

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

### Solution

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### Problem 2

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

\(0\)

\(1\)

\(\frac17\)

\(7^0\)

\(7^{10}\)

### Solution

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### Problem 3

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

\(1^6\)

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

\(3^4\)

\(3^6\)

### Solution

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### Problem 4

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

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

### Solution

### Problem 5

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