Question 28
The value of $$\left(\frac{\sqrt{10}}{10}\right)^{(\log_{10} 9) - 2}$$ is of the form $$\frac{a}{b}$$, where $$a, b$$ are relatively prime to each other. Then $$a - b$$ is equal to
Correct Answer: 7
Solution
Since $$\frac{\sqrt{10}}{10} = 10^{-1/2}$$, the expression is $$10^{-\frac{1}{2}(\log_{10} 9 - 2)} = 10^{-\frac{1}{2}\log_{10} 9} \times 10 = \frac{10}{\sqrt{9}} = \frac{10}{3}$$. Hence $$a = 10$$, $$b = 3$$ and $$a - b = 7$$.
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