Exponents and Powers (NCERT Ch. 13)

• Express numbers using exponential notation (base and exponent).
• Apply the laws of exponents: product rule, quotient rule, power rule, zero exponent.
• Express large numbers in standard form (scientific notation).

1. aᵐ x aⁿ = aᵐ⁺ⁿ (product rule — same base, add exponents).
2. aᵐ ÷ aⁿ = aᵐ⁻ⁿ (quotient rule — same base, subtract exponents).
3. (aᵐ)ⁿ = aᵐⁿ (power rule — multiply exponents).
4. a⁰ = 1 (any nonzero base raised to power 0 equals 1).
5. Standard form: a number written as k x 10ⁿ, where 1 ≤ k < 10.

Simplify: 2³ x 2⁴

Same base, add exponents: 2³ x 2⁴ = 2^(3+4) = 2⁷ = 128

• Adding exponents when the bases are different (only valid for the same base).
• Multiplying the base by the exponent instead of using repeated multiplication (2³ = 2x2x2 = 8, NOT 2x3=6).
• Forgetting a⁰ = 1 (not 0).

• Simplify: 5⁶ ÷ 5².
• Write 45,000 in standard form.

Open the Practice tab for graded questions on Exponents and Powers (NCERT Ch. 13).