Q1
What is a^m × a^n?
Aa^(m+n)
Ba^(m×n)
Ca^(m-n)
Da^m
ICSEClass 9 (ICSE)MathematicsCh 7 · Topic 1
Indices (Exponents)
Indices (exponents) represent repeated multiplication, and laws of indices help us simplify expressions with powers efficiently.
Core concept
The laws of indices include: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m-n), (a^m)^n = a^(mn), and a^0 = 1 (for non-zero a).
How it works
A negative index, like a^(-n), equals 1/a^n, representing a reciprocal rather than a negative value.
Why it matters
A fractional index, like a^(1/n), represents the nth root of a, so a^(1/2) means the square root of a.
Key detail
Mastering index laws is essential for simplifying complex expressions and solving equations involving powers.
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• a^m × a^n = a^(m+n).
• a^m ÷ a^n = a^(m-n).
• (a^m)^n = a^(mn).
• a^0 = 1 for non-zero a.
• Negative index: a^(-n) = 1/a^n.
• Fractional index: a^(1/n) = nth root of a.
• a^(1/2) means square root of a.
• Index laws simplify complex expressions.