Exponent
- CBSE · NCERT Class 8 Part 1, Ch 2 Power Play
An exponent is the small raised number that says how many copies of the base are multiplied together, so 2⁵ means 2 × 2 × 2 × 2 × 2.
An exponent, also called a power, is a short way to write repeated multiplication. In 2⁵, the base is 2 and the exponent is 5. It means 2 × 2 × 2 × 2 × 2 = 32. We read it as "2 to the power 5".
A few rules follow from this meaning:
- Same base, multiplied: add the exponents. 3² × 3⁴ = 3⁶.
- Same base, divided: subtract them. 5⁷ ÷ 5³ = 5⁴.
- A power of a power: multiply them. (2³)² = 2⁶.
- Any non-zero number to the power 0 is 1.
A small example
Write 360 using exponents. Break it into primes: 360 = 2 × 2 × 2 × 3 × 3 × 5. Group the equal primes. That gives 360 = 2³ × 3² × 5.
A common slip is to treat 2³ as 2 × 3. It is 2 × 2 × 2, which is 8, not 6.
Why it matters later
Class 10 Chapter 1 writes every prime factorisation with exponents. To find the HCF you take the smallest power of each common prime. For the LCM you take the greatest power of each prime. See HCF and LCM. Both steps depend on reading exponents correctly.
Sources
Facts last checked against these sources on 30 September 2026.
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