Question

express 108 X 192 as a product of prime factor in exponential form

Answer 1

Answer:

$Product \: of \: 108 \times 192 =2^{8}\times 3^{4}$

Step-by-step explanation:

Resolving 108 and 192 into product of prime factors,we get

2| 108

______

2| 54

______

3| 27

______

3| 9

______

** 3

108 = 2² × 3³

2| 192

______

2| 96

______

2| 48

______

2| 24

______

2| 12

______

2| 6

______

*** 3

$192 = 2^{6}\times 3^{1}$

$Now, \\Product \: of \: 108 \times 192 \\= 2^{2}\times 3^{3}\times 2^{6}\times 3^{1}\\=2^{2+6}\times 3^{3+1}$

$By\: Exponential\: Law :\\\boxed {a^{m}\times a^{n} = a^{m+n}}$

$= 2^{8}\times 3^{4}$

Therefore,

$Product \: of \: 108 \times 192 =2^{8}\times 3^{4}$

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Answer 2

Answer:

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