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Property 6

Evaluate:2-1+...

Question

Evaluate:
$(2^{- 1} + 3^{- 1})^{3}$

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Solution

$Given (2^{- 1} + 3^{- 1})^{3} (\frac{1}{2} + \frac{1}{3}) [∵ a^{- m} = \frac{1}{a^{m}}] = {(\frac{3 + 2}{6})}^{3} [LCM of (2,3) is 6] = {(\frac{5}{6})}^{3} = \frac{5 \times 5 \times 5}{6 \times 6 \times 6} = \frac{125}{216} Hence, the value of given expression is \frac{125}{216}$ .

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Q. 13)evaluate (x+1)√2x^2+3

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