For p = {3, 5, 10, 15}, q = {1,6, 13}, and r = {4, 6, 10, 13}, find p u (q∩r).

 P U (Q∩R)={3, 5, 6, 10, 13, 15}

Step-by-step explanation:

The first step that we have to do is find  (Q∩R) then, we ned to find the elements in common between Q and R, as we can see we have the element 6 and the element 13, then:

(Q∩R)={6, 13}

Now we just need to do the union between  P and  (Q∩R), that is just put all the elements of P and  (Q∩R) in one set, then:

P U (Q∩R)={3, 5, 6, 10, 13, 15}

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: