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Encapsulate
math

ExpoNENtS aNd poWErS

If a is any integer and n is a natural number, then Scientific Notation
n
a = a × a × a × a × . . . n times
n
In a , a is the base and n is the exponent or power. A number is said to be in standard form if it is
m
expressed as a × 10 , where 1 ≤ a < 10 and m is
a = a × a × a × a × . . . n times an integer.
n
Exponential Expanded or E.g., 324,000,000 = 3.24 × 100,000,000 = 3.24 × 10 8
form Product form

Laws of Exponents

For any non-zero integers a and b, and m and n are whole numbers,

n
m
Law 1: a × a = a m + n Law 2: a ÷ a = a m – n
m
n
m n
mn
Law 3: (a ) = a Law 4: (a × b) = a × b m
m
m
a
Law 5:    m = a m Law 6: For any non-zero integer a with exponent n = 0, a = 1
0

b
m
b
maths fun
Puzzle
Across

3
1. 5.724 × 10 is the standard form of ................ .
1 6 7
3
5
21 × 10 × 125
2. The value of is ................ .
5
3
2 × 3 × 5 8 8 2
3. The value of 2 5×2–3–2 is ................ . 10 9 3
2
2
4. The value of 11 – 3 – 11 is ................ .
4
5. The number 10 is the exponential form of ................ .
3
5
Down
6. The value of 3 is ________.
5
3
2
4
7. The value of 4 × 10 + 3 × 10 + 2 × 10 + 7 × 10 is ................ .
8. The square of 21 is ................ .
2
9. The value of (11) – 20 is ................ .
10. In 2 44 , the exponent of 2 is ................ .
8

93 Exponents and Powers