The value of frac{1.073 times 1.073 - 0.927 t | vedclass

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Question

(C) Let the expression be $E = \frac{1.073 	imes 1.073 - 0.927 	imes 0.927}{1.073 - 0.927} + \frac{(3^4)^4 	imes (9)^6}{(27)^7 	imes (3)^9}$.Using

Vedclass · Accepted Answer

$2\frac{1}{9}$

Vedclass · Answer

(C) Let the expression be $E = \frac{1.073 	imes 1.073 - 0.927 	imes 0.927}{1.073 - 0.927} + \frac{(3^4)^4 	imes (9)^6}{(27)^7 	imes (3)^9}$.Using the identity $a^2 - b^2 = (a+b)(a-b)$,the first part becomes:$\frac{(1.073)^2 - (0.927)^2}{1.073 - 0.927} = \frac{(1.073 + 0.927)(1.073 - 0.927)}{1.073 - 0.927} = 1.073 + 0.927 = 2.000 = 2$.For the second part,express all terms with base $3$:$\frac{(3^4)^4 	imes (3^2)^6}{(3^3)^7 	imes 3^9} = \frac{3^{16} 	imes 3^{12}}{3^{21} 	imes 3^9} = \frac{3^{16+12}}{3^{21+9}} = \frac{3^{28}}{3^{30}} = \frac{1}{3^{30-28}} = \frac{1}{3^2} = \frac{1}{9}$.Adding both parts: $2 + \frac{1}{9} = 2\frac{1}{9}$.

The value of $\frac{1.073 \times 1.073 - 0.927 \times 0.927}{1.073 - 0.927} + \frac{(3^4)^4 \times 9^6}{(27)^7 \times 3^9}$ is

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