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Question

Question 98(ii)

Simplify:
((23)2)3×(13)4×31×16

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Solution

Using the laws of exponents,
(am)n=(a)m×n,=am×an=am+n and am÷an=amn

((23)2)3×(13)4×31×16

=(23)2×3×(3)4×13×16

=(23)6×34×13×12×3

=(32)6×34×13×2×3=(3)6(2)6×34×121×32

​​​​​​​=(3)6×(3)4(1)6(2)6×(2)1×(3)2

=(3)6+4(2)6+1×32=(3)1027×32

=310227=3827


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