Page 2 - Home Assignment -Introduction-Ch-13 Exponents ane powers

Expanding Decimal Numbers Using Powers

A given rational number can be expressed in expanded form with the help
of exponents.
Consider a number 1204.65.
1204.65=1000+200+4+0.6+0.05=(1×10³)+(2×10²)+(0×10¹)+(4×10-¹)+(5×10-²)

Laws of Exponents

>Exponents with like Bases

n
m
Given a non-zero integer a, a ×a =a m+n where m and n are integers.
m
n
and a ÷a =a m−n where m and n are integers.
7
7−3
10
3
3
7
For example: 2 ×2 = 2 7 + 3 = 2 and 2 ÷ 2 = 2
>Power of a Power
m n
mn
Given a non-zero integer a, (a ) = a , where m and n are integers.
4 3
12
For example: (2 ) = 2 4×3 = 2 Given a non-zero integer a,
0
(a) = 1 Any number to the power 0 is always 1.
>Exponents with Unlike Bases and Same Exponent
Given two non-zero integers a and b,

m
m
m
a ×b = (a×b) , where m is an integer.
3
3
3
3
For example: 2 ×5 = (2×5) = 10 = 1000
Useful Link:
https://www.youtube.com/watch?v=gx3ejuvQjR4
https://www.youtube.com/watch?v=N7KyotcCYRw
https://www.youtube.com/watch?v=N7KyotcCYRw

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