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))

Bytelearn · Accepted Answer

Simplify base of expression: Simplify the base of the expression. We have the expression ((8^(-5))/(2^(-2)))^(-4). We can simplify the base by recognizing that 8 is 2^3. So, we can rewrite 8^(-5) as (2^3)^(-5).Apply power of a power rule: Apply the power of a power rule. Using the power of a power rule, (a^b)^c = a^(b*c), we can simplify (2^3)^(-5) to 2^(3*(-5)) = 2^(-15).Simplify denominator of base: Simplify the denominator of the base. Now we simplify 2^(-2). Since the exponent is negative, it is equivalent to 1/(2^2) = 1/4.Combine numerator and denominator: Combine the simplified numerator and denominator. We now have (2^(-15))/(1/4), which is the same as 2^(-15) * 4. Since 4 is 2^2, we can write this as 2^(-15) * 2^2.Apply product of powers rule: Apply the product of powers rule. Using the product of powers rule, a^m * a^n = a^(m+n), we combine 2^(-15) * 2^2 to get 2^(-15+2) = 2^(-13).Apply negative exponent to entire base: Apply the negative exponent to the entire base. Now we have (2^(-13))^(-4). Using the power of a power rule again, we get 2^(-13 * -4) = 2^(52).Rewrite expression in terms of original base 8: Rewrite the expression in terms of the original base 8. Since 8 is 2^3, we want to express 2^(52) in terms of a power of 8. We can divide the exponent by 3 to find the equivalent power of 8: 52 ÷ 3 = 17 with a remainder of 1. So, 2^(52) = (2^3)^(17) * 2^1 = 8^(17) * 2.Choose correct answer: Choose the correct answer from the given options. We have 8^(17) * 2, which is not in the form of any of the answer choices. This indicates a mistake has been made in the previous steps. We need to re-evaluate our calculations.

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

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