Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Rewrite negative integer exponents without changing the sign of the base.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Evaluate 2⁻³ and (−2)⁻³.
Why this math matters
Read very small scale factors as reciprocals of large positive powers. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Interpret negative powers as reciprocals
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Evaluate 2⁻³ and (−2)⁻³.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
2⁻³ = 1/2³
A negative exponent names the reciprocal of a positive power.
Develop the calculation
(−2)⁻³ = 1/(−2)³
Parentheses keep the negative sign inside the base.
Check and interpret
2⁻³ = 1/8; (−2)⁻³ = −1/8
An odd power preserves the negative base sign; the negative exponent itself does not make a positive base negative.
The result
2⁻³ = 1/8; (−2)⁻³ = −1/8
An odd power preserves the negative base sign; the negative exponent itself does not make a positive base negative.
Common mistakes to catch
- A negative exponent does not mean a negative product.
- Negative powers require a nonzero base.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Evaluate 5⁰ and 5⁻².
Show a hint
A nonzero base to zero is one; a negative power uses its reciprocal.
Reveal answer and explanation
1 and 1/25
The rules preserve the quotient law as powers decrease.
Practice 2
Why is 0⁻¹ undefined?
Show a hint
Rewrite it as a reciprocal.
Reveal answer and explanation
It would be 1/0
No real number multiplied by zero equals one, so zero has no reciprocal.
Take the idea with you
Read very small scale factors as reciprocals of large positive powers.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Keep scale and significant factor separate
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