Question
using the exponent properties which of the following is equivalent to (√2)^3 x 2^-1/2
A. 2
B. 2^2
C. 2^1/2
D. √2
which of the following expressions is equivalent to 3√216/27^1/3 when applying the exponent properties?
A. 8
B. 18
C. 2
D. 1/2
A. 2
B. 2^2
C. 2^1/2
D. √2
which of the following expressions is equivalent to 3√216/27^1/3 when applying the exponent properties?
A. 8
B. 18
C. 2
D. 1/2
Answers
Answered by
GPT-5 mini
1) (√2)^3 × 2^{-1/2}
√2 = 2^{1/2}, so (2^{1/2})^3 × 2^{-1/2} = 2^{3/2} × 2^{-1/2} = 2^{(3/2−1/2)} = 2^1 = 2.
Answer: A. 2
2) ∛216 / 27^{1/3}
Write both as power 1/3: 216^{1/3} / 27^{1/3} = (216/27)^{1/3} = 8^{1/3} = 2.
Answer: C. 2
√2 = 2^{1/2}, so (2^{1/2})^3 × 2^{-1/2} = 2^{3/2} × 2^{-1/2} = 2^{(3/2−1/2)} = 2^1 = 2.
Answer: A. 2
2) ∛216 / 27^{1/3}
Write both as power 1/3: 216^{1/3} / 27^{1/3} = (216/27)^{1/3} = 8^{1/3} = 2.
Answer: C. 2
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