elementary-math Module
Interactive Simulation Screen
SYS_OKLesson Directive // Exponents & RootsREF_CORE
What Is a Power?
Hover over a variable in the formula above, or see glossary below:
Base
Real Number
Exponent / Power
Integer
a^n means the base a is multiplied by itself n times. For example, 2^4 = 2 \times 2 \times 2 \times 2 = 16.
INSIGHT: Exponentiation is repeated multiplication, just as multiplication is repeated addition.
Key Exponent Laws
a^m \times a^n = a^{m+n} (same base, add exponents). (a^m)^n = a^{mn} (power of a power). a^0 = 1 for any a \ne 0.
INSIGHT: The laws of exponents let you simplify complex expressions without computing huge numbers.
Square & Cube Roots
The square root \sqrt{a} is the inverse of squaring: \sqrt{9} = 3 because 3^2 = 9. Roots are fractional exponents: \sqrt{a} = a^{1/2}.
INSIGHT: $\sqrt{a} = a^{1/2}$ — roots are just fractional exponents.