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 distinguish a power of a power from a product.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Exponent multiplication rules.
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
Expand and simplify (2x³)². Explain why the coefficient and exponent change differently.
Why this math matters
Raising a power to another integer power multiplies the exponents, and an outside power acts on every factor of a product. Identify whether parentheses contain a product or a sum before applying an exponent rule.
Set up the model
A useful answer starts with clear assumptions:
- x is real.
- The outer square applies to the entire parenthesized product.
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.
Distinguish a power of a power from a product
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Expand and simplify (2x³)². Explain why the coefficient and exponent change differently.
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
(2x³)² = (2x³)(2x³)
A square repeats the whole grouped quantity twice.
Apply the relationship
(2×2)(x³x³) = 4x⁶
Multiply coefficients normally and add exponents of the common base x.
Check and interpret
(2x³)² = 2² × x^(3×2) = 4x⁶
The compact rule multiplies the inner exponent by the outer exponent.
The result
(2x³)² = 2² × x^(3×2) = 4x⁶
The compact rule multiplies the inner exponent by the outer exponent.
Common mistakes to catch
- Squaring a product does not leave its numerical coefficient unchanged.
- (a + b)² is a sum inside parentheses, so it needs distribution rather than the product-power rule.
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 (a²)⁴.
Show a hint
Count four copies of a².
Reveal answer and explanation
a⁸
The total exponent is 2 × 4 = 8.
Practice 2
Simplify (−3y²)³.
Show a hint
Cube the signed coefficient as well as the variable factor.
Reveal answer and explanation
−27y⁶
(−3)³ = −27 and (y²)³ = y⁶.
Take the idea with you
Identify whether parentheses contain a product or a sum before applying an exponent rule.
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: Extend exponent patterns through zero
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