Laws of Exponents (Integral Powers) MCQs Quiz | Class 9

Test your understanding of Class IX Mathematics (Code 041), Unit I: Number Systems. This quiz covers the Laws of Exponents (Integral Powers), including recalling and applying laws like a^m * a^n, a^m/a^n, (a^m)^n, (ab)^n, and (a/b)^n. Complete the quiz to view your score and download the PDF answer key.

Overview: Laws of Exponents

Exponents (or powers) provide a shorthand way to write repeated multiplication. In Class 9, mastering the integral powers of real numbers is crucial for simplifying algebraic expressions and solving equations. The laws of exponents apply to non-zero bases and integer exponents.

Key Laws of Exponents

For any non-zero real numbers a and b, and integers m and n:

  • Product Law: a^m * a^n = a^(m+n) (Add exponents when multiplying like bases)
  • Quotient Law: a^m / a^n = a^(m-n) (Subtract exponents when dividing like bases)
  • Power of a Power: (a^m)^n = a^(mn) (Multiply exponents)
  • Power of a Product: (ab)^n = a^n * b^n (Distribute exponent to factors)
  • Power of a Quotient: (a/b)^n = a^n / b^n (Distribute exponent to numerator and denominator)

Special Cases

Rule Formula Example
Zero Exponent a^0 = 1 (where a is not 0) 5^0 = 1
Negative Exponent a^(-n) = 1 / a^n 2^(-3) = 1/8

Quick Revision Tips

  • Always check if the bases are the same before applying product or quotient laws.
  • Any non-zero number raised to the power of 0 is always 1. Beware of expressions like -5^0 vs (-5)^0.
  • When simplifying, try to express composite numbers as powers of prime bases (e.g., 32 = 2^5).

Extra Practice Questions

Try solving these on paper:

  1. Simplify: (2^3 * 3^4 * 4) / (3 * 32)
  2. Find x if 2^(x-7) * 5^(x-4) = 1250
  3. Evaluate: (25)^(3/2) * (243)^(3/5) / (16)^(5/4) * (8)^(4/3)
  4. Simplify: (x^a / x^b)^(a+b) * (x^b / x^c)^(b+c) * (x^c / x^a)^(c+a)
  5. If 4^x – 4^(x-1) = 24, find (2x)^x.