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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Encapsulate
math
ExPONENtS aND POWERS

Exponent
2 10
Base

Exponential Form Laws of Exponents

Repeated multiplication of a number by itself in Law 1: Multiplying powers with the same base
short form.
n
m
a × a = a m + n
Law 2: Dividing powers with the same base
• x × x × x × x ... 10 times = x 10 m
n
m
−
• x × x × x × x ... n times = x n a ÷ a = a a n = a mn
1
• x = x
m
• (–x) is positive if m is an even number, negative Law 3: Power of a power mn
m n
if m is an odd number. (a ) = a
Law 4: Multiplying powers with the same exponents
m
Expanded Form a × b = (ab) m
m
Law 5: Dividing powers with the same exponents
–2
0
25.368 = 2 × 10 + 5 × 10 + 3 × 10 + 6 × 10 + 8 × 10 –3 m m
–1
1
a
a ÷ b = a m =   
m
m

Scientific Notation or Standard Form b b
A number is said to be in the scientific notation if Powers with zero exponent
it is in the form
n
k × 10 , where 1 ≤ k < 10 and n is an integer. Any non-zero base raised to the power 0 is 1, i.e.,
0
Example: (a) 138400000 = 1.384 × 10 8 a = 1.
(b) 0.000000287 = 2.87 × 10 –7
Powers with negative exponents
1
For any non-zero integer a, a − n = , where n is an integer.
a n

Mental Maths
0
1. Find the multiplicative inverse of 3(7 – 1) .
2
2. Simplify the ratio 8 : 4 4.
)
)
)
3. What is the value of (x a + b (a – b) × (x b + c (b – c) × (x c + a (c – a) ?
4. Find the value of a, if (x × x × x × x × x × x ) = 1.
5 a
2
4
3
0
4 − 4
5. Rewrite using only the positive exponent.
5 − 2
6. Human body has approximately 100 billion cells. Write it in exponential form.
7. What is the standard form of 1234000000?
8. What is the usual form for 5.03 × 10 ?
–5
273 Exponents and Powers