Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Explanation Of Exercise 1.4

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Unit 1: Real And Complex Numbers
Explanation Of Exercise 1.4

Explanation Of Laws of Exponents/Indices

 Laws of Exponents/Indices: 

Laws of exponents or indices are important in many fields of mathematics.

Recall Base, Exponent and value of Power
Consider an exponential form aⁿ here, 'a' is called the base and 'n' is called exponent or index i.e., read as a to the nth power. The result of aⁿ, where a ∈ R is called its value.

Apply the Laws of Exponents to Simplify Expressions with Real Exponents
The following laws of exponents are useful to simplify the expressions.

(i) Law of Product of Powers

• (a) If a, b ∈ R and x, y ∈ Z⁺
• Then, a^x x a^y = a^x+y

Some examples based on this law are given below:

• (a) a² x a³ = a²⁺³ = a⁵
• (b) 3 x 3⁵ = 3¹⁺⁵ x 3⁶ = 729

(ii) Law of Power of Power
If a ∈ R and x, y ∈ Z⁺, then (a^x)^y = a^xy
Some examples based on this law are given below:

• (a) (5²)⁴ = 5^2x4 = 5⁸ = 390625