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Question

Sort the following numbers in increasing order from top to bottom.
  1. (42)3
  2. (32)4
  3. (23)3
  4. (42)2


Solution

The correct option is
By using law of exponent:
(am)n=amn Here a is called the base and m,n are called the exponent. For Power of power exponents are multiplied if the base is same.
 (42)3=46
                        =(4×4×4×4×4×4)
=(4××4×4)×(4××4×4)
=64×64
=4096

 (32)4=38
                        =(3×3×3)×(3×3×3)×(3×3)
=(27××27×9)
=729×9
=6561

 (23)3=29
                        =(2×2×2×2)×(2×2×2)×(2×2)
=(16××8×4)
=128×4
=512

 (42)2=44
                        =(4×4×4×4)
=(4×4)×(4×4)
=16×16
=256

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