Year 9
Mathematics
Number & Algebra
AC9M9N02
Advanced Index Laws
Index laws extend to negative, zero, and fractional exponents. These rules simplify expressions involving powers and roots.
What You Need to Know
Key Concept Diagram
a^0 = 1 for any non-zero a
a^(-n) = 1/a^n (negative exponent means reciprocal)
a^(1/n) = nth root of a (fractional exponent)
a^(m/n) = (nth root of a)^m = nth root of a^m
Key Vocabulary
Index (exponent)
The power to which a base is raised
Zero exponent
Any non-zero base to the power 0 equals 1
Negative exponent
Indicates a reciprocal: a^-n = 1/a^n
Fractional exponent
Represents a root: a^(1/n) is the nth root of a
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Evaluate 5^(-2).
Question 2
Simplify 27^(1/3).
Question 3
Evaluate 8^(2/3).
Key Concepts Summary
- ●a^0 = 1 for any non-zero a
- ●a^(-n) = 1/a^n (negative exponent means reciprocal)
- ●a^(1/n) = nth root of a (fractional exponent)
- ●a^(m/n) = (nth root of a)^m = nth root of a^m