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x=(((1)/(2))/(2+2))/((2+2+2)/((2+2+2)/(2)))

$x=\frac{\frac{\frac{1}{2}}{2+2}}{\frac{2+2+2}{\frac{2+2+2}{2}}}$

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Multiplication with rational exponents

Full solution

Q.

x=\frac{\frac{\frac{1}{2}}{2+2}}{\frac{2+2+2}{\frac{2+2+2}{2}}}

Simplify numerator: Step $1$ : Simplify the numerator. $\newline$ We start by simplifying the innermost parentheses in the numerator. $\newline$ Calculation: $(\frac{1}{2}) / (2 + 2) = (\frac{1}{2}) / 4 = \frac{1}{8}$
Simplify denominator: Step $2$ : Simplify the denominator. $\newline$ Next, simplify the denominator by handling the inner division first. $\newline$ Calculation: $(2 + 2 + 2) / ((2 + 2 + 2) / 2) = 6 / (6 / 2) = 6 / 3 = 2$
Divide numerator by denominator: Step $3$ : Divide the simplified numerator by the simplified denominator. $\newline$ Now, divide the results from Step $1$ and Step $2$ . $\newline$ Calculation: $(\frac{1}{8}) / 2 = \frac{1}{8} * \frac{1}{2} = \frac{1}{16}$

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