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Posted: January 28th, 2022
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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)
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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.
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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
At least 50 words should be included in your response.
RESPONSE OF PEERS:
I wish everyone a happy and healthy New Year's Eve. For this week's conversation, I am #20, with difficulties #28 and #40.
# 28) 16, Evaluate the Expression Using the Strategy a
The first step is to write 16 in square form. 4 is the primary square root of 16.
Consequently, = (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
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