Class 9 Mathematics
Chapter: Logarithms & Exponents
Full Chapter Summary Notes
Part 1 — Exponents (Indices)
Definition
An exponent (or index/power) tells how many times a base is multiplied by itself.
Written as a^n, where 'a' is the base and 'n' is the exponent.
Example: 2^4 = 2 x 2 x 2 x 2 = 16
Laws of Exponents
Product Rule: a^m x a^n = a^(m+n)
Quotient Rule: a^m / a^n = a^(m-n)
Power Rule: (a^m)^n = a^(m*n)
Zero Exponent: a^0 = 1 (where a != 0)
Negative Exponent: a^(-n) = 1 / a^n
Fractional Exponent: a^(1/n) = nth root of a
Product of Bases: (a*b)^n = a^n x b^n
Quotient of Bases: (a/b)^n = a^n / b^n
Worked Examples
Q: Simplify 3^2 x 3^4
A: = 3^(2+4) = 3^6 = 729
Q: Simplify (2^3)^^4
A: = 2^^4 = 2^(6-4) = 2^2 = 4
Q: Find the value of 5^(-2)
A: = ^2 = 1/25
Q: Simplify (27)^(1/3)
A: = cube root of 27 = 3
Common Mistakes
WARNING: You can ONLY add/subtract exponents when the BASES are the same.
WARNING: a^m x b^m = (a*b)^m — only works when exponents are the same, NOT the
bases.
Chapter: Logarithms & Exponents
Full Chapter Summary Notes
Part 1 — Exponents (Indices)
Definition
An exponent (or index/power) tells how many times a base is multiplied by itself.
Written as a^n, where 'a' is the base and 'n' is the exponent.
Example: 2^4 = 2 x 2 x 2 x 2 = 16
Laws of Exponents
Product Rule: a^m x a^n = a^(m+n)
Quotient Rule: a^m / a^n = a^(m-n)
Power Rule: (a^m)^n = a^(m*n)
Zero Exponent: a^0 = 1 (where a != 0)
Negative Exponent: a^(-n) = 1 / a^n
Fractional Exponent: a^(1/n) = nth root of a
Product of Bases: (a*b)^n = a^n x b^n
Quotient of Bases: (a/b)^n = a^n / b^n
Worked Examples
Q: Simplify 3^2 x 3^4
A: = 3^(2+4) = 3^6 = 729
Q: Simplify (2^3)^^4
A: = 2^^4 = 2^(6-4) = 2^2 = 4
Q: Find the value of 5^(-2)
A: = ^2 = 1/25
Q: Simplify (27)^(1/3)
A: = cube root of 27 = 3
Common Mistakes
WARNING: You can ONLY add/subtract exponents when the BASES are the same.
WARNING: a^m x b^m = (a*b)^m — only works when exponents are the same, NOT the
bases.
