# GSEB Class 8 Maths Notes Chapter 12 Exponents and Powers

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°.