Lesson 7
Negative Exponents
- Let’s explore numbers with negative exponents.
7.1: Math Talk: Powers of Ten
Solve each equation mentally:
\frac{100}{1}=10^x
\frac{1000}{x}=10^1
\frac{x}{100}=10^0
\frac{100}{1000}=10^x
7.2: Maintain the Pattern
Complete the table.
| exponential form | number form | calculations | |
|---|---|---|---|
| 2^5 | |||
| 16 | |||
| \frac{2^4}{2}=2^{4-1}=2^3 | 2^3 | ||
| \frac{2^3}{2}=2^{3-1}=2^2 | 2^2 | 4 | |
| 2 | 4 \boldcdot \frac12=2 | ||
| 1 | 2 \boldcdot \frac12=1 | ||
| 2^{\text-1} | \frac{1}{2} | ||
| \frac{1}{4} | \frac12 \boldcdot \frac12 = \frac14 | ||
| 2^{\text-3} | |||
| 2^{\text-4} | |||
| \frac{1}{32} |
7.3: Matching Equal Expressions
Take turns with your partner to match the original expression with an equal or equivalent expression in the list.
- For each match that you find, explain to your partner how you know it’s a match.
- For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
Which expressions equal 8^0?
- 1
- 0
- 8^3 \boldcdot 8^{-3}
- \frac{8^2}{8^2}
- 11^0
Which expressions equal 5^{\text-2}?
- \text-5^2
- \frac{5^{0}}{5^2}
- \text-2^5
- \frac{1}{5^2}
- 5^{\text-1} \boldcdot 5^{\text-1}
Which expressions equal 3^{10}?
- 3^5\boldcdot3^2
- \left(3^5\right)^2
- 3^7 \boldcdot 3^3
- 3^{13} \boldcdot 3^{\text-3}
- \frac{3^{10}}{3^{0}}
Which expressions are equivalent to x^{\text-4}?
- \frac{x^9}{x^5}
- \frac{x^5}{x^9}
- \frac{x^{3}}{x^{-1}}
- x\boldcdot x^{\text-5}
- \frac{1}{x^4}