Exponent Lab
Slide the exponents and watch each rule expand into repeated multiplication — the product, quotient, and power rules as living factor-counting.
1 Exponent Lab
Two sliders, one rule at a time. The lab writes out the full expansion so you can count the factors yourself.
Each box is one factor of x · blue/teal: the two groups · struck boxes cancel in a quotient.
2 What to notice
Three experiments.
1. Count the product
Set a = 3, b = 2 on the product rule: the expansion shows 5 x’s — 3 + 2.
2. Cancel the quotient
Set a = 4, b = 2 on the quotient rule: pairs cancel, leaving 4 − 2 = 2 factors.
3. Group the power
Set a = 2, b = 3 on the power rule: three groups of two — 2 · 3 = 6 factors.