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What is the simplified form of
((2^(3))/(4^(2)))^(2) ?

What is the simplified form of $\left(\frac{2^{3}}{4^{2}}\right)^{2}$ ?

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Evaluate rational exponents

Full solution

Q. What is the simplified form of

\left(\frac{2^{3}}{4^{2}}\right)^{2}

?

Rewrite as $2$ squared: Rewrite $4$ as $2$ squared, so $4^2$ becomes $(2^2)^2$ .
Calculate exponent for $2$ : Calculate the exponent for $2$ in the denominator, $(2^2)^2 = 2^{(2*2)} = 2^4$ .
Simplify expression: Now the expression is $((2^3)/(2^4))^2$ .
Subtract exponents: Simplify the fraction inside the parentheses by subtracting the exponents, $2^3 / 2^4 = 2^{(3-4)} = 2^{-1}$ .
Raise to power of $2$ : Raise $2^{-1}$ to the power of $2$ , $(2^{-1})^2 = 2^{-1*2} = 2^{-2}$ .
Simplify result: Simplify $2^{-2}$ to $1/(2^2)$ .
Calculate final answer: Calculate $2^2$ , which is $4$ .
Calculate final answer: Calculate $2^2$ , which is $4$ .So the final answer is $\frac{1}{4}$ .

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