Question

3. Express the following as a product of prime factors
in exponential form. a. 108 x 64 b. 288 x 324​

Answer 1

Answer:

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}192=2

6

×3

1

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

Now,

Productof108×192

=2

2

×3

3

×2

6

×3

1

=2

2+6

×3

3+1

\begin{gathered}By\: Exponential\: Law :\\\boxed {a^{m}\times a^{n} = a^{m+n}}\end{gathered}

ByExponentialLaw:

a

m

×a

n

=a

m+n

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

8

×3

4

Therefore,

Product \: of \: 108 \times 192 =2^{8}\times 3^{4}Productof108×192=2

8

×3

4

•••♪

Answer 2

I DID NOT UNDERSTAND YOUR QUESTION!