root(3)(64^(27)) Which of the following is equivalent to the given expression? Choose 1 answer: (A) 4^(3) (B) 64^(3) (c) 8^(18) (D) 64^(24)

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root(3)(64^(27)) Which of the following is equivalent to the given expression? Choose 1 answer: (A)  4^(3) (B)  64^(3) (c)  8^(18) (D)  64^(24)

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Understand the expression: Understand the given expression root(3)(64^(27)). This expression is asking for the cube root of 64 raised to the 27th power.Simplify the base: Simplify the base 64 to a power of 2. Since 64 is 2 raised to the 6th power (2^6), we can rewrite 64^(27) as (2^6)^(27).Apply power of a power rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). Therefore, (2^6)^(27) becomes 2^(6*27).Calculate the exponent: Calculate the exponent. Multiply the exponents: 6*27 = 162. So, 2^(6*27) is 2^162.Apply the cube root: Apply the cube root to the expression. The cube root of 2^162 is the same as 2^(162/3) because root(3)(a^m) = a^(m/3).Calculate the new exponent: Calculate the new exponent. Divide the exponent by 3: 162/3 = 54. So, 2^(162/3) is 2^54.Determine the correct choice: Determine which answer choice matches 2^54. We need to find an answer choice that is equivalent to 2^54. Let's examine the choices: (A) 4^3 is 2^6, which is not equal to 2^54. (B) 64^3 is (2^6)^3, which is 2^18, not 2^54. (C) 8^18 is (2^3)^18, which is 2^54, so this is the correct choice. (D) 64^24 is (2^6)^24, which is 2^144, not 2^54.

$\sqrt[3]{64^{27}}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $4^{3}$ $\newline$ (B) $64^{3}$ $\newline$ (C) $8^{18}$ $\newline$ (D) $64^{24}$

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64273 \sqrt[3]{64^{27}} 36427​\newlineWhich of the following is equivalent to the given expression?\newlineChoose 111 answer:\newline(A) 43 4^{3} 43\newline(B) 643 64^{3} 643\newline(C) 818 8^{18} 818\newline(D) 6424 64^{24} 6424

$\sqrt[3]{64^{27}}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $4^{3}$ $\newline$ (B) $64^{3}$ $\newline$ (C) $8^{18}$ $\newline$ (D) $64^{24}$