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 :
- am × an = am+n where m and n are integers. am
- \(\frac{a^{m}}{a^{n}}\) = am-n where a ≠ 0, m > n
\(\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}\) = an-m where a ≠ 0, m < n
\(\frac{a^{m}}{a^{n}}\) = am-n – a0 = 1 where m – n, a ≠ 0 - (am)n = amn where n is natural number.
- am × bm = (ab)m, \(\left(\frac{a}{b}\right)^{m}=\frac{a^{m}}{b^{m}}\) where b ≠ 0
- a-n = \(\frac{1}{a^{n}}\) and an = \(\frac{1}{a^{-n}}\) 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 × 105
- 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°.