Question
Using the exponent properties, which of the following expressions is equivalent to (2–√)^3⋅2−^1/2?(1 point)
Responses
2
2
2–√
Start Root 2 End Root
212
2 superscript Start Fraction 1 over 2 End Fraction baseline
22
Responses
2
2
2–√
Start Root 2 End Root
212
2 superscript Start Fraction 1 over 2 End Fraction baseline
22
Answers
Answered by
GPT 3.5
To simplify the expression (2–√)^3⋅2−^1/2 using exponent properties, we can apply the rule that states (a^m)^n = a^(m*n).
First, let's simplify (2–√)^3:
(2–√)^3 = (2–√)(2–√)(2–√)
Using the distributive property, we can expand this expression:
= (2–√) * (2–√ * 2–√)
= (2–√)*(2–√ * 2)
= (2–√)*(2–2√)
= (2–√)*(2 – 2√ + 2√ – 2) (using the distributive property again)
= (2–√)*(0)
= 0
Now let's simplify 2^(-1/2):
2^(-1/2) = 1/(2^(1/2)) = 1/√2
Therefore, the expression (2–√)^3⋅2−^1/2 simplifies to:
0 * 1/√2 = 0
So the correct response is 0.
First, let's simplify (2–√)^3:
(2–√)^3 = (2–√)(2–√)(2–√)
Using the distributive property, we can expand this expression:
= (2–√) * (2–√ * 2–√)
= (2–√)*(2–√ * 2)
= (2–√)*(2–2√)
= (2–√)*(2 – 2√ + 2√ – 2) (using the distributive property again)
= (2–√)*(0)
= 0
Now let's simplify 2^(-1/2):
2^(-1/2) = 1/(2^(1/2)) = 1/√2
Therefore, the expression (2–√)^3⋅2−^1/2 simplifies to:
0 * 1/√2 = 0
So the correct response is 0.
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