🧱 What IS an Exponent?
- x³ means x × x × x (multiply x by itself 3 times). BIG number = BASE. Small raised = EXPONENT.
- 2⁴ = 2×2×2×2 = 16 | x⁰ = 1 ALWAYS! | x¹ = x | x⁻² = 1/x² (flip it!)
MULTIPLY Same Base
xᵃ · xᵇ = xᵃ⁺ᵇ
- ADD the exponents
- x³ · x² = x⁵
DIVIDE Same Base
xᵃ ÷ xᵇ = xᵃ⁻ᵇ
- SUBTRACT exponents
- x⁵ ÷ x² = x³
POWER of a Power
(xᵃ)ᵇ = xᵃˣᵇ
- MULTIPLY exponents
- (x³)² = x⁶
ZERO Exponent
x⁰ = 1
- ALWAYS equals 1
- 99⁰ = 1
NEGATIVE Exponent
x⁻ᵃ = 1/xᵃ
- Flip to the bottom!
- x⁻² = 1/x²
POWER of Product
(xy)ᵃ = xᵃyᵃ
- Spread the power
- (2x)³ = 8x³
🔢 Desmos Strategies
3 Ways to Get the Answer!
Strategy 1: Evaluate / Find a Value
- Type with CAPITAL letters
- e.g. 2^A * 2^B
- Add sliders for A and B
- Set A=3, B=2 → answer = 32
- Then type 2^(A+B) → also 32
- Same value = law is correct!
Strategy 2: Graph / Visualize
- Type in lowercase to graph
- y = 2^x (exponential curve)
- y = x^2 (parabola)
- Compare their shapes!
- See how fast each grows
- Observe x-intercepts
Strategy 3: Generate Table
- Type y = 2^x → click Table
- See how y DOUBLES each step
- x: 0,1,2,3 → y: 1,2,4,8
- Confirm simplified answer
- by checking table values match
- original expression values!
Remember This!
- Rules ONLY work with SAME base: x³ · x² = x⁵ BUT x³ · y² CANNOT be combined!
- ADDING exponents (x² + x³) does NOT simplify — only MULTIPLYING uses the laws!
- Any number to the power 0 = 1. Negative exponent = flip the base to the bottom (reciprocal).