The distance between the Sun and the earth is 149,600,000,000m. It’s very difficult to read and even to write also. To make these type of numbers easy to read and write we use exponents. Using exponents the same number can be written as 1496×108m. Here we read 108 as 10 raised to the power 8. An exponent is mathematically defined as follows.
“The exponent of a number shows how many times that number is multiplied in a product”.
An exponent is also called as power.
Example:
22 = 2×2
35 = 3x3x3x3x3
Laws of indices: For any real numbers x and y,
(1) xm x xn = x m+n
Example:
22 x 23 = 4 x 8 = 32 = 25
This property can be remembered as “The powers of same bases must be added in case of multiplication”.
(2) xm / xn = x m-n
Example:
23 / 22 = 8 / 4 = 2 = 21 = 23-2
This property can be remembered as “The powers of same bases must be subtracted in order in case of division”.
(3) x-m = 1/xm
Example:
2-3= 1/23 = 1/8
This property can be remembered as “a negative (positive) power can be converted into negative (positive) by taking its reciprocal.”
(4) x0 =1, where x ≠ 0.
Example:
30 = 31-1 = 31/31 = 1
This property can be remembered as “Any number raised to zero is always one”.
(5) (xm)n = xmn
Example:
(32)3 = 93 = 243=36.
This property can be remembered as “The powers of same base must be multiplied”.
(6) xm x ym = (xy)m
Example:
23 x 33 = 8 x 27 = 216 = 63= (2×3)3
This property can be remembered as “The product of different bases of same multiplied can be written as the product of bases raised to the same power”.
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