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Learning by Doing

a
b
Objective: To understand law of exponents x ÷ x = x a – b , a > b
Materials Required: Chart paper, sketch pen, ruler, etc.
Procedure:
• Take an expression 2 ÷ 2 = 2 = 8
3
5
2
• Take a rectangular glazed paper and fold it halves as many times as the power of dividend.
Here, dividend is raised to power 5. So, we have to fold it 5 times as shown below:

• Unfold the paper and count the number of rectangles.
2
• Then, make groups of boxes equal to divisor using sketch pen. Here divisor is 2 = 4.

• Now, count the number of boxes in each group obtained.
Observation: The number of boxes in each group is equal to the quotient.
2
3
3
5
So, 2 ÷ 2 = 2 = 8, 2 = 2 5 –2 .
b
Hence x ÷ x = x a–b .
a
Brain Sizzlers

1. Suppose if you have a stretching machine which could stretch almost anything. For example, if you put a 5
3
metre stick into a (× 4 ) stretching machine, you will get a 320 metre stick and a shrinking machine where
3
4
a piece of stick is compressed to reduce its length by (÷ 3 ). If 54 cm long sandwich is put into the (× 4 )
4
stretching machine, and then (÷3 ) shrinking machine, how long (in cm) will it be when it emerges?
25
a
2. If 125 = , then what is the value of 6a + 10b?
3125 b
277 Exponents and Powers