Chapter – 13

Exponents and Powers

Power is the product of multiplying a number by itself. It shows how many times the base is multiplied by itself.
The base number tells what number is being multiplied.
The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.
The number 5 is called the base, and the number 2 is called the exponent.
An exponent is a small number written above and to the right of the base number, tells how many times the base number is being multiplied.
The base a raised to the power of is equal to the multiplication of a, n times:
a
aa...a = an
a is the base and n is the exponent.

For example, “3 to the power 4” may be written as 34. Here, the base number is 3, and the exponent is 4. It means that 3 is being multiplied by itself 4 times: 3 x 3 x 3 x 3.
Where,
3 x 3 x 3 x 3 = 81 or 34 81.
The positive value of a positive integer is always positive.
A negative number is positive if the multiplier is an even number and negative if the multiplier is an odd number.

• 'a' square or 'a' in the second stage:

a2=aa

• 'a' cube or 'a' in the third stage:

a3= a⋅  a⋅  a

• 'a' in the fourth stage:

a4 = a⋅  a⋅  a⋅  a

A fraction with a whole negative multiplier is taken to be a fraction with a numerator of 1, but the denominator is the same base with the opposite positive multiplier.

a−n=1an (n−naturalnumbers)

anam=an + m;an:am = an−m,n> m,a ≠ 0;(an)m=anm

Where n and m are integers.

The normal form of a number is called the multiple of this number: a10nwhere1 ≤ a < 10

Note that greater than 1 and less than 10.

When dividing degrees with the same base, the powers are subtracted, and the base remains unchanged.

an:am=an−m

Where a≠0, n and m are natural numbers such that n>m.

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###### Medha Sharma

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