Select the equivalent expression. ((8^(-5))/(2^(-2)))^(-4)=? Choose 1 answer: (A) (8^(20))/(2^(8)) (B) (2^(6))/(8^(9)) (C) (1)/(8*2^(2))

Question

Select the equivalent expression.  ((8^(-5))/(2^(-2)))^(-4)=? Choose 1 answer: (A)  (8^(20))/(2^(8)) (B)  (2^(6))/(8^(9)) (C)  (1)/(8*2^(2))

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Identify and Apply Rule: Identify the given expression and apply the power of a quotient rule. The power of a quotient rule states that (a/b)^n = a^n / b^n. So, ((8^(-5))/(2^(-2)))^(-4) becomes (8^(-5))^(-4) / (2^(-2))^(-4).Simplify Exponents: Simplify the exponents by multiplying them, since (a^m)^n = a^(m*n). For the numerator, (8^(-5))^(-4) becomes 8^((-5)*(-4)) = 8^(20). For the denominator, (2^(-2))^(-4) becomes 2^((-2)*(-4)) = 2^(8).Rewrite Simplified Expression: Rewrite the simplified expression. The expression is now 8^(20) / 2^(8).Recognize Power of 2: Recognize that 8 is a power of 2, specifically 8 = 2^3. This allows us to express 8^(20) as (2^3)^(20).Apply Power of Power Rule: Apply the power of a power rule to simplify (2^3)^(20). The rule states that (a^m)^n = a^(m*n), so (2^3)^(20) becomes 2^(3*20) = 2^(60).Rewrite with Simplified Numerator: Rewrite the expression with the simplified numerator. The expression is now 2^(60) / 2^(8).Apply Quotient of Powers Rule: Apply the quotient of powers rule to simplify 2^(60) / 2^(8). The rule states that a^m / a^n = a^(m-n), so 2^(60) / 2^(8) becomes 2^(60-8) = 2^(52).Recognize Simplified Form: Recognize that 2^(52) is the simplified form of the original expression. Therefore, the equivalent expression is 2^(52).Match to Answer Choices: Match the simplified expression to the given answer choices. The expression 2^(52) is not directly listed in the answer choices, so we need to check if any of the choices are equivalent to 2^(52).Check for Equivalence: Check each answer choice for equivalence to 2^(52). (A) (8^(20))/(2^(8)) is equivalent to 2^(60)/2^(8) = 2^(52), which matches our simplified expression. (B) (2^(6))/(8^(9)) is not equivalent to 2^(52). (C) (1)/(8*2^(2)) is not equivalent to 2^(52).Select Correct Answer: Select the correct answer choice based on the previous step. The correct answer is (A) (8^(20))/(2^(8)), which is equivalent to 2^(52).

Select the equivalent expression. $\left(\frac{8^{-5}}{2^{-2}}\right)^{-4}=\,?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{8^{20}}{2^{8}}$ $\newline$ (B) $\frac{2^{6}}{8^{9}}$ $\newline$ (C) $\frac{1}{8\cdot 2^{2}}$

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Select the equivalent expression. (8−52−2)−4= ?\left(\frac{8^{-5}}{2^{-2}}\right)^{-4}=\,?(2−28−5​)−4=?\newlineChoose 111 answer:\newline(A) 82028\frac{8^{20}}{2^{8}}28820​\newline(B) 2689\frac{2^{6}}{8^{9}}8926​\newline(C) 18⋅22\frac{1}{8\cdot 2^{2}}8⋅221​

Select the equivalent expression. $\left(\frac{8^{-5}}{2^{-2}}\right)^{-4}=\,?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{8^{20}}{2^{8}}$ $\newline$ (B) $\frac{2^{6}}{8^{9}}$ $\newline$ (C) $\frac{1}{8\cdot 2^{2}}$