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PEERS RESPONSE:

I hope everyone had a safe and healthy New Year’s. I am #20 for this week’s discussion; problems #28 and # 40. 

I will start with # 28) 16, Evaluate the Expression Using the Strategy  a

The first step is to write 16 as a perfect square. The principal square root of 16 would be 4.

So, = (42)

Next, I need to eliminate the exponents using the rule of exponents (xa)b=x(a⋅b) ……..a=2, b=3/2

= (42) = 43  the exponents 2 and denominator 2 are eliminated which leaves me with =43. Final step is to solve 4 to the third power which equals 64. This is my answer.

For the second problem, #40)  3 5  

To solve I used the product rule for radicals because both radicals are of the same index. The 
nth root 
of a product will be equal to the product of the 
nth roots. 

First, I need to get all radicals under a single square root. This would look like: 

Next is to multiply 3 by 6, then add the exponents 3&5.

      =   This is the radical form. This still needs to be simplified. Factor out the terms.

Now 18 and b8 needs to be written as a multiple of a perfect square. The two numbers whose product is 18 would be 9*2 and the two numbers whose product is 8 is 4*2. So, I get the following:

 = 2 To simplify I must cancel exponents and the                                         square root.

=   2 The sqrt of 9 is 3^2,  =

=3b4 Finally, we need to reorder the terms to get, 

= 3 This is the answer.

Thanks, Erica