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

Practice Time 11A

1. Write the base and exponents of each of the following.
 −  2 3 1
(a) (–5) 4 (b) (9) 8 (c)   5   (d) 4 5
2. Write the following in exponential form.
2 2 2 2 2 2
(a) 6 × 6 × 6 × 6 × 6 (b) (–4) × (–2) × (–2) × (–2) × (–4) (c) × × × × ×
5 5 5 5 5 5
3. Simplify and express the result in exponential form.
2

3
 2 7  2 2      −   2   2
3
10
(a) 3 × 3 × 3 2 (b) (–25) × (–25) 10 (c)   ×   (d)    7    


9
9


 
 

2
2
10
5
5
(e) 5 × 10 (f) (2) × (4) 10 (g)    7 ÷    2 (h) (–7) × (3) 4
4
4. Simplify.  7   7 
−  3
−  4
× b
25
5
6
(
(a) a × ) 3 (b) 25 × a 2 5 × b 4 4 (c)    6   2 ×    4   2 (d)    9 ×    5 ×    − 36  
a
5
4
5
5 × a
6


5. Find the value of x in each of the following.
 5 2  5 14  5 8x − ( ) 2 9 2x −1
(a) 5 = 125 (b) 4 x+4 = 1024 (c)   ×   =   (d) =− ( ) 2
x
 2  2  2 − ( ) 2 2
Power with Zero Exponent
When the terms containing the same base and same exponent are divided, we get a zero exponent.
For example,
5 7 5 7
7
7
5 ÷ 5 = = 5 7 – 7 = 5 . Also, 5 ÷ 5 = = 1 ⇒ 5 = 1
7
0
0
7
5 7 5 7
Any non-zero base raised to the power 0 is 1.
0
Thus, in general, for any non-zero integer a, a = 1.
Powers with Negative Exponents
When the terms containing exponents are continuously divided by the base, we get the result that
has negative exponents after some steps.
Observe the given pattern:
10 000
,
3
10 = 10 × 10 × 10 = 1000 =
10
1000
10 = 10 × 10 = 100 =
2
10
100
1
10 = 10 =
10
10
0
10 = 1 =
10
265 Exponents and Powers