3. represents the sets with a venn diagram: u = {1,2,3,4,5,6,7,8,9, 10, 11, 12} a = {1,2,3,4,6, 12} b = {1,2,4,8}

See explanation and picture attached

Step-by-step explanation:

A set can be described by listing all of its elements.  

For example, A = { 2, 4, 6, 8}, which we read as  

“A is the set whose elements are 2, 4, 6 and 8”.  

The four elements of the set are separated by commas, and the list is enclosed between curly brackets.  

A set can also be described by writing a description of its elements between curly brackets.  

Thus the set A above can also be written as  

A = { even natural numbers less than 9 }, which we read as  

“A is the set of even natural numbers less than 9”.  

A set can also be described graphically by using Venn diagrams, which are simply circle shaped drawings showing the elements inside.

In our case U={1,2,3,4,5,6,7,8,9,10,11,12} A={1,2,3,4,6,12} B={1,2,4,8}

See picture attached for the answer.

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: