Which of the following is equal to this expression? (256·64)^1/4 A) 4·\sqrt[4]{4} B) 8·\sqrt[4]{4} C) 8·\sqrt[4]{2} D) 2·\sqrt[4]{2}

asked Oct 15, 2023 58.3k views

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Which of the following is equal to this expression?

(256·64)^1/4
A) 4·
$\sqrt[4]{4}$
B) 8·
$\sqrt[4]{4}$
C) 8·
$\sqrt[4]{2}$
D) 2·
$\sqrt[4]{2}$

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7 votes

Answer:

B)
$8\sqrt[4]{4}$

Explanation:

$(2^(8) *2^(6) )^(1)/(4) = (2^(8+6) )^(1)/(4) =(2^(14) )^(1)/(4) =2^{(7)/(2) }=\sqrt{2^(7) } =2^(3) √(2) =8√(2) = 8\sqrt[4]{2^(2) } = 8\sqrt[4]{4}$

FridayPush answered Oct 21, 2023

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