A power (or index) tells us how many times to multiply a number by itself.
2³ = 2 × 2 × 2 = 8
5² = 5 × 5 = 25
4¹ = 4
3⁰ = 1 (any number⁰ = 1)
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐˣⁿ
a⁻ⁿ = 1/aⁿ
Roots are the opposite of powers. They ask "what number, when raised to this power, gives us this result?"
√16 = 4
Because 4² = 16
∛27 = 3
Because 3³ = 27
1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
Standard form (scientific notation) is a way to write very large or very small numbers more easily.
Where: 1 ≤ a < 10 and n is an integer
Large Numbers:
45,000 = 4.5 × 10⁴
7,200,000 = 7.2 × 10⁶
Small Numbers:
0.0034 = 3.4 × 10⁻³
0.000056 = 5.6 × 10⁻⁵
1. Calculate: 2⁴
2. Express 340,000 in standard form