Learn with Amar
Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to count factors to combine powers.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Positive integer powers and multiplication.
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
Simplify (3⁴ × 3²)/3³ and explain the exponent arithmetic by counting factors.
Why this math matters
Multiplication adds exponents of a common base, while division cancels matching nonzero factors. Write powers as repeated factors when you are unsure which exponent rule applies.
Set up the model
A useful answer starts with clear assumptions:
- All powers have the same base, 3.
- The divisor is nonzero.
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.
Count factors to combine powers
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Simplify (3⁴ × 3²)/3³ and explain the exponent arithmetic by counting factors.
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 quantities
3⁴ × 3² = 3⁶
Four factors of 3 followed by two more create six factors.
Apply the relationship
3⁶/3³ = 3³
Cancel three factors from numerator and denominator.
Check and interpret
3³ = 27; combined exponent = 4 + 2 − 3
Adding and subtracting exponents summarizes the factor count.
The result
3³ = 27; combined exponent = 4 + 2 − 3
Adding and subtracting exponents summarizes the factor count.
Common mistakes to catch
- Add exponents only when multiplying powers with a common base.
- Cancelling a variable factor requires that factor to be nonzero.
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
Simplify x⁵x²/x³ for x ≠ 0.
Show a hint
Combine the exponent counts before evaluating.
Reveal answer and explanation
x⁴
5 + 2 − 3 = 4; the nonzero condition allows cancellation.
Practice 2
Is 2³ + 2² equal to 2⁵?
Show a hint
The exponent product law requires multiplication, not addition.
Reveal answer and explanation
No: 12 differs from 32
2³ + 2² = 8 + 4 = 12, while 2⁵ = 32.
Take the idea with you
Write powers as repeated factors when you are unsure which exponent rule applies.
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: Distinguish a power of a power from a product
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