5. What is the perimeter of the algebra tile figure? Enter the simplified algebraic expression. *

4x + 16

Step-by-step explanation:

Since the area of the light blue square is x^2, we know that 2 of the sides are equivalent to x. Since the shape is a square, we now know that ALL sides are x. So the perimeter of the light blue square is 4x.

Each square with an area of 1(dark blue squares), tells us that each side is equivalent to 1. This means that the perimeter is 1+1+1+1. Since we have 4 copies of this type of square, we can write 4 x 4 = 16.

Therefore, our final simplified algebraic equation is 4x + 16.

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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:

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