Select the equivalent expression. ((2^(-10))/(4^(2)))^(7)=? Choose 1 answer: (A) (1)/(2^(70)*4^(14)) (B) 2^(84) (c) 2^(-3)*4^(-9)

Question

Select the equivalent expression.  ((2^(-10))/(4^(2)))^(7)=? Choose 1 answer: (A)  (1)/(2^(70)*4^(14)) (B)  2^(84) (c)  2^(-3)*4^(-9)

Bytelearn · Accepted Answer

Simplify base: Simplify the base of the exponent. We have the expression ((2^(-10))/(4^(2)))^(7). First, we need to simplify the base. Since 4 is 2^2, we can rewrite 4^2 as (2^2)^2.Power rule: Apply the power of a power rule. Using the power of a power rule, which states that (a^(m))^n = a^(m*n), we can simplify (2^2)^2 as 2^(2*2) = 2^4.Rewrite expression: Rewrite the original expression with the simplified base. Now we can rewrite the original expression as ((2^(-10))/(2^4))^(7).Quotient rule: Apply the quotient of powers rule. Using the quotient of powers rule, which states that a^(m)/a^(n) = a^(m-n), we can simplify the expression inside the parentheses as 2^(-10-4) = 2^(-14).Power rule again: Apply the power of a power rule again. Now we have (2^(-14))^(7). Using the power of a power rule again, we can simplify this as 2^(-14*7) = 2^(-98).Check answer choices: Check the answer choices. We have simplified the expression to 2^(-98). Now we need to check which answer choice matches this expression. (A) (1)/(2^(70)*4^(14)) does not match because it has positive exponents and includes a factor of 4^(14). (B) 2^(84) does not match because it has a positive exponent and the exponent is different from -98. (C) 2^(-3)*4^(-9) does not match because it has two separate bases and the exponents do not add up to -98. None of the answer choices match our simplified expression.

Select the equivalent expression. $\newline$ $((2^{-10})/(4^{2}))^{7}=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $(1)/(2^{70}\cdot4^{14})$ $\newline$ (B) $\newline$ $2^{84}$ $\newline$ (C) $\newline$ $2^{-3}\cdot4^{-9}$

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Select the equivalent expression.\newline((2−10)/(42))7=?((2^{-10})/(4^{2}))^{7}=?((2−10)/(42))7=?\newlineChoose 111 answer:\newline(A) \newline(1)/(270⋅414)(1)/(2^{70}\cdot4^{14})(1)/(270⋅414)\newline(B) \newline2842^{84}284\newline(C) \newline2−3⋅4−92^{-3}\cdot4^{-9}2−3⋅4−9

Select the equivalent expression. $\newline$ $((2^{-10})/(4^{2}))^{7}=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $(1)/(2^{70}\cdot4^{14})$ $\newline$ (B) $\newline$ $2^{84}$ $\newline$ (C) $\newline$ $2^{-3}\cdot4^{-9}$