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 = 10^{4}

8 × 8 × 8 × 8 × 8 × ….. × 8 (16 times) = 8^{16}.

→ 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 = 2^{4} Here 2 is base 4 is exponent.

3 × 3 × 3 × 3 × 3 = 3^{5} 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} × a^{n} = a^{m+n}

ii) (a^{m})^{n} = a^{mn}

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

iv) a^{m} = a^{n} ⇒ 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) a^{0} = 1 where a ≠ 0