AP Board 7th Class Maths Notes Chapter 11 Exponents

Students can go through AP Board 7th Class Maths Notes Chapter 11 Exponents to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 11 Exponents

→ Very large numbers are easier to read, write and understand when expressed in exponential form.
Eg : 10000 = 10⁴
8 × 8 × 8 × 8 × 8 × ….. × 8 (16 times) = 8¹⁶.

→ When a number is multiplied by itself for many number of times (repeated multiplication) then we write it in exponential form.
Eg : 2 × 2 × 2 × 2 = 2⁴ Here 2 is base 4 is exponent.
3 × 3 × 3 × 3 × 3 = 3⁵ Here 3 is base 5 is exponent.

→ a . a . a . a ….. a (m times) = a^m.

→ Here ‘a’ is called the base and ‘m’ is called the exponent.

→ Laws of exponents

i) a^m × aⁿ = a^m+n

ii)  (a^m)ⁿ = a^mn

iii) (ab)^m = a^m . b^m

iv) a^m = aⁿ ⇒ m = n

v) a^-n = \(\frac{1}{a^{n}}\)

vi) \(\frac{\mathrm{a}^{\mathrm{m}}}{\mathrm{a}^{\mathrm{n}}}\) = a^m-n  if (m > n)
= \(\frac{1}{a^{n-m}}\)  if (m < n)
= 1 if (m = n)

vii) \(\left(\frac{a}{b}\right)^{m}\) = \(\frac{a^{m}}{b^{m}}\)

viii) a⁰ = 1 where a ≠ 0