Exponents — Formula Sheet
ICSE · Class 7 · Mathematics
18 formulas from Exponents (ICSE Class 7 Mathematics) on one page, grouped by topic. Part of the ICSE Class 7 Mathematics syllabus.
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Formulas and Key Relations
1. Core Meaning and Notation
a^n = a × a × a × a × ... × a
5^7
(-3)^8
2. Numbers in Exponential Form
625 = 5^4
32 = 2^5
729 = 3^6
3. Laws of Exponents
a^m × a^n = a^(m + n)
a^m / a^n = a^(m-n) if m > n; a^m / a^n = 1/a^(n-m) if m < n
(a^m)^n = a^(mn)
(ab)^m = a^m b^m
(a/b)^m = a^m / b^m
4. Zero Index and Negative Index
a^0 = 1, if a ≠ 0
a^-m = 1/a^m and 1/a^-m = a^m
Exponential Form of Numbers
625 = 5 × 5 × 5 × 5 = 5^4.
32 = 2 × 2 × 2 × 2 × 2 = 2^5.
729 = 3 × 3 × 3 × 3 × 3 × 3 = 3^6.
Key relations
For example, 2^6 = 64, 8^3 = 512, 5^6 = 15625, and 3^5 = 243.
For the same base, a^m × a^n = a^(m+n).
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