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Step-by-step explanation:

Reflection over the line x=a is the transformation ...

  (x, y) ⇒ (2a -x, y)

Then the double reflection over x=a and x=b is the transformation ...

  (x, y) ⇒ (2b -(2a -x), y) = (2(b-a) +x, y)

That is, the result is translation by twice the distance between the lines. For a=1 and b=3, the transformation is ...

  (x, y) ⇒ (x +4, y) . . . . . . . translation to the right by 4 units.

  A(-5, 2) ⇒ A''(-1, 2)

  B(-1, 5) ⇒ B''(3, 5)

  C(0, 3) ⇒ C''(4, 3)

step-by-step explanation:

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: