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, (a^b)^c = a^(b*c), we can simplify (2^2)^2 as 2^(2*2) which is 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, a^(m)/a^(n) = a^(m-n), we can simplify the base as 2^(-10-4) which is 2^(-14).Power rule: Apply the power of a power rule to the entire expression. Now we apply the power of a power rule to the entire expression (2^(-14))^(7), which simplifies to 2^(-14*7).Multiply exponents: Multiply the exponents. Multiplying the exponents -14 and 7 gives us 2^(-98).Compare with choices: Compare the result with the answer choices. The expression 2^(-98) is equivalent to 1/(2^(98)). This does not match any of the answer choices directly, so we need to check if we can rewrite it to match one of the options.Rewrite using exponents: Rewrite the expression using properties of exponents. We can rewrite 2^(-98) as 2^(-70) * 2^(-28). Since 2^(-28) is equal to 1/(2^(28)) and 2^(28) is equal to 4^(14) (because 2^(2*14) = 4^(14)), we can rewrite the expression as 1/(2^(70) * 4^(14)).Match with choices: Match the rewritten expression with the answer choices. The rewritten expression 1/(2^(70) * 4^(14)) matches answer choice (A).

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

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Select the equivalent expression.\newline(2−1042)7=? \left(\frac{2^{-10}}{4^{2}}\right)^{7}=? (422−10​)7=?\newlineChoose 111 answer:\newline(A) 1270⋅414 \frac{1}{2^{70} \cdot 4^{14}} 270⋅4141​\newline(B) 284 2^{84} 284\newline(C) 2−3⋅4−9 2^{-3} \cdot 4^{-9} 2−3⋅4−9

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