# Exponents and Powers-Notes

Class VIII Math

Notes for Exponents and Powers
FACTS THAT MATTER
The numbers with negative exponents also obey the following laws:
(i) xm × xn = xm + n
(ii) xm ÷ xn = xm – n
(iii) xm × bm = (xb)m
(ii) x0 = 1

A number is said to be in the standard Form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10.
Very small numbers can be expressed in standard form using negative exponents.
WE KNOW THAT
When we write 54, it means 5 × 5 × 5 × 5, i.e. 5 is multiplied 4 times. So 5 is the base and 4 is the exponent. We read 54 as �5 raised to the power 4�.
We also know the following laws of exponents
(i) xm × xn = xm + n
(ii) xm ÷ xn = xm – n
(iii) xm)n = xm × n
(iv) xm × ym = (xy)m

The value of any number raised to 0 is 1, i.e. a0 = 1.
We express very small or very large numbers in standard form (i.e scientific notation) for example:

POWER WITH NEGATIVE EXPONENTS
For a non-zero integer x, we have

or x�m × xm = 1
So x�m is the reciprocal (or the multiplicative inverse) of xm and vice versa.
For example: (i) Reciprocal of 8�7 = 87 and
(ii) Reciprocal of 87 = 8�7