This GSEB Class 8 Maths Notes Chapter 12 Exponents and Powers covers all the important topics and concepts as mentioned in the chapter.

## Exponents and Powers Class 8 GSEB Notes

→ Laws of exponents :

- a
^{m}× a^{n}= a^{m+n}where m and n are integers. am - \(\frac{a^{m}}{a^{n}}\) = a
^{m-n}where a ≠ 0, m > n

\(\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}\) = a^{n-m}where a ≠ 0, m < n

\(\frac{a^{m}}{a^{n}}\) = a^{m-n}– a^{0}= 1 where m – n, a ≠ 0 - (a
^{m})^{n}= a^{mn}where n is natural number. - a
^{m}× b^{m }= (ab)^{m}, \(\left(\frac{a}{b}\right)^{m}=\frac{a^{m}}{b^{m}}\) where b ≠ 0 - a
^{-n}= \(\frac{1}{a^{n}}\) and a^{n}= \(\frac{1}{a^{-n}}\) where a ≠ 0

→ It is difficult to read, write and compare very small and very large numbers.

→ So standard form is used to represent them.

e.g.

- 1,50,000 = 1.5 × 1,00,000 = 1.5 × 10
^{5} - 0.0025 = \(\frac{25}{10000}\) = 2.5 × 10 × 10
^{-4}

= 2.5 × 10^{-3}

Thus, very small numbers can be expressed in standard form using negative exponents. Standard form is also called scientific notation.

→ How to express given number in the standard form?

- Shift the decimal point in the given number so that only one non-zero digit should be before the decimal point and rest all the digits after the decimal point.
- Count the number of digits over which the decimal point is shifted.
- If the decimal is shifted to the left of its original position, write this number as power of 10 in standard form.
- If the decimal is shifted to the right of its original position, write the negative of this number as power of 10.
- If the given number is between 1 and 10 then we write it as the product of the number itself and 10°.