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Negative Indices Exploration
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Negative Indices Exploration
Answer each question. Show working where asked. Give fractional answers in simplest form.
Understanding Negative Indices
1.Which expression is equivalent to 3⁻⁴?
- −3 × −3 × −3 × −3
- 1 ÷ (3 × 3 × 3 × 3)
- 3 × 3 × 3 × 3
- −1 ÷ (3 × 3 × 3 × 3)
2.Select every expression equal to 4⁻².
- 1/16
- 1/(4²)
- (1/4)²
- −16
3.Evaluate 5⁻². Show how you use the negative index rule.
4.Fill in the missing values in the sequence of powers of 6: 6³ = 216, 6² = 36, 6¹ = 6, 6⁰ = , 6⁻¹ = , 6⁻² = .
Converting and Calculating
5.Write 9⁻¹ as a fraction.
6.Write 3⁻⁴ as a fraction in simplest form.
7.Write 10⁻² as a fraction in simplest form.
8.Evaluate 7⁻².
9.Evaluate 2⁻⁶.
10.Evaluate 8⁻¹.
11.A sample contains 160 mg of a substance. Its amount after h hours is modelled by A = 160 × 2⁻ʰ mg. Find the amount after 1 hour and after 4 hours.
Applying Negative Indices
12.A model for a cooling drink is T = 72 × 3⁻ᵗ⁄¹² °C, where t is the time in minutes. Use the model to find T when t = 12 minutes.
13.In your own words, describe what a negative index tells you. Include one numerical example.
14.Solve for x: 5⁻² × 5ˣ = 5³. Show your reasoning.
3 printable pages
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