What’s the difference between the following points using Pythagorean theorem

√29

Step-by-step explanation:

(5, 10) and (10, 12) are separated horizontally by (10 - 5), or 5.  This is the length of the horizontal leg of a triangle.

They are separated vertically by (12 - 10), or 2.  This is the vertical leg length.

The distance (not difference) between the two points is then

(distance) = √( 5^2 + 2^2 ), or √(25 + 4), or √29

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: