Find a ∩ b if a = {3, 6, 9, 12} and b = {2, 4, 6, 8, 10, 12}.

The set A ∩ B contain {6, 12}

Step-by-step explanation:

Given : set A = {3, 6, 9, 12} and set B = {2, 4, 6, 8, 10, 12}

We have to find A ∩ B

Consider the given sets

Set A = {3, 6, 9, 12}

and set B = {2, 4, 6, 8, 10, 12}

Since, A ∩ B  includes those elements that are both in set A and set B.

Thus, the common elements of A and B are 6 and 12

So , the set A ∩ B contain {6, 12}

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: