Grade 8 · Exponents
Balance ledger: Explain zero and negative powers
Balance ledger investigation: explain zero and negative powers. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
An integer exponent records repeated multiplication for positive powers and repeated division for negative powers. The starting value at exponent zero is one. A negative exponent forms a reciprocal and does not make a positive base negative. This investigation begins with positive base = 6; integer exponent = -1. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
a⁰=1; aⁿ=a×…×a; a⁻ⁿ=1/aⁿ
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Start at exponent zero with value one and choose a positive, nonzero base.
- STEP 2
Follow the changing model
Playback advances through whole exponent steps. A positive target multiplies by the base; a negative target divides by it.
- STEP 3
Check and explain the relationship
Compare the completed result with its reciprocal when changing only the exponent sign.
Your turn to explain
Make a prediction. Test your reasoning.
Balance ledger: Evaluate 6 to the integer power -1.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
0.167. Use the reciprocal of the corresponding positive power.
Work through a full lesson
Connect the animation to a worked example and practice questions.