Indices — Chapter Summary
ICSE · Class 9 · Mathematics
Summary of Indices for ICSE Class 9 Mathematics. Part of the ICSE Class 9 Mathematics syllabus. Indices express repeated multiplication in a compact form.
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Overview
Indices express repeated multiplication in a compact form. For a positive integer m, a×a×a×... up to m terms is written as a^m, where a is the base and m is the power, exponent, or index. This notation makes large calculations shorter and helps in working with powers, roots, and algebraic simplifica
Key Concepts
a^m means a multiplied by itself
a^m means a multiplied by itself m times. Here, a is the base and m is the power, exponent, or index.
When powers have the same base
When powers have the same base, multiplication adds the indices: a^m × a^n = a^(m+n). The printed form in the chapter is a^m × a^m = a^(m+m), and exam
When powers have the same base
When powers have the same base, division subtracts the indices: a^m ÷ a^n = a^(m-n).
A power raised to another power
A power raised to another power means the indices are multiplied: (a^m)^n = a^(mn).
(a×b)^m = a^m × b^m
(a×b)^m = a^m × b^m and (a/b)^m = a^m / b^m.
Learning Objectives
- Understand index notation and identify the base and exponent.
- Use the Product Law, Quotient Law, and Power Law of indices.
- Work with positive, fractional, negative, and zero indices.
- Convert between radical form and fractional index form.
- Simplify expressions using laws of indices.
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