Indices
The law of indices explains how powers behave when numbers are multiplied, divided, or raised to another power. It is a core topic in TU CMAT algebra and arithmetic simplification.
Practice MCQs for Indices
Fundamental Principles
Index (Exponent)
An index or exponent shows how many times a number is multiplied by itself. Example: a^n means a is multiplied n times.
Base
The number that is multiplied repeatedly in an exponential expression.
Power
The result of raising a base to an exponent.
Essential Formulation Tips
- Always check if bases are same before applying rules.
- Convert negative exponents into fractions first.
- Break complex expressions into smaller parts.
- Use exponent rules instead of full multiplication.
Shortcut Execution Techniques
- a^m × a^n → add exponents
- a^m ÷ a^n → subtract exponents
- (a^m)^n → multiply exponents
- a^-n → flip to denominator
- a^0 → always 1
Contextual Inquiries (FAQs)
Q: Why is a^0 = 1?
A: Because dividing same powers cancels out, leaving 1.
Q: What happens with negative exponents?
A: They become reciprocals of positive exponents.
Q: Where are indices used in CMAT?
A: In simplification, algebra, and exponential equations.
Example Breakdown: Product Rule
Basic CMAT indices questionAdd exponents
2^(3+4) = 2^7 = 128
Example Breakdown: Quotient Rule
Common exam questionSubtract exponents
5^(6-2) = 5^4 = 625
Example Breakdown: Power of Power
Important CMAT ruleMultiply exponents
3^(2×3) = 3^6 = 729
Example Breakdown: Negative Exponent
Frequently asked trick questionTake reciprocal
1 / 2^3 = 1/8
CMAT Laws of Indices Basics Set 1
Fundamental exponent rules and basic simplification problems.
Q1. a^2 × a^3 = ?
Q2. a^6 ÷ a^2 = ?
Q3. (a^3)^2 = ?
Q4. a^0 = ? (a ≠ 0)
Q5. a^1 = ?
Q6. 2^3 × 2^2 = ?
Q7. 5^4 ÷ 5^1 = ?
Q8. (x^2)^3 = ?
Q9. 10^0 = ?
Q10. 3^2 × 3^3 = ?