Question

Use the laws of exponents and simplify: $\frac{(12)^6}{162}$

Answer 1

Solution :

2 | 162
_______
3 | 81
_______
3 | 27
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3 | 9
_______
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162 = 2 × 3⁴

12 = 2² × 3

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We know the Exponential laws:

i ) ( a^m )ⁿ = a^mn

ii ) a^m/a^n = a^m-n
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Now ,

( 12 )^6/162

= [ ( 2² × 3 )^6 ]/( 2 × 3⁴ )

= [ ( 2² )^6 × 3^6 ]/( 2 × 3⁴ )

= ( 2^12 × 3^6 )/( 2¹ × 3⁴ )

= 2^12-1 × 3^6-4

= 2^11 × 3²

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Answer 2

hope this helps.........