If we multiply a fraction by itself and divid | vedclass

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Question

(C) Let the fraction be $x$.According to the problem,we multiply the fraction by itself and divide by the square of its reciprocal:$x 	imes x \div \l

Vedclass · Accepted Answer

$\frac{4}{3}$

Vedclass · Answer

(C) Let the fraction be $x$.According to the problem,we multiply the fraction by itself and divide by the square of its reciprocal:$x 	imes x \div \left(\frac{1}{x}ight)^2 = 3 \frac{13}{81}$Convert the mixed fraction to an improper fraction:$3 \frac{13}{81} = \frac{3 	imes 81 + 13}{81} = \frac{243 + 13}{81} = \frac{256}{81}$Now,simplify the equation:$x^2 \div \frac{1}{x^2} = \frac{256}{81}$$x^2 	imes x^2 = \frac{256}{81}$$x^4 = \frac{256}{81}$Express the right side as a power of $4$:$x^4 = \left(\frac{4}{3}ight)^4$Therefore,$x = \frac{4}{3}$.

If we multiply a fraction by itself and divide the product by the square of its reciprocal,the fraction obtained is $3 \frac{13}{81}$. The original fraction is

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