Given ${log}_{10} a = b$ , express $10^{2 b - 3}$ in terms of $a$ .

\frac{a^{2}}{10}

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\frac{a^{2}}{100}

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\frac{a^{2}}{1000}

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\frac{a^{2}}{10000}

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Solution

The correct option is C $\frac{a^{2}}{1000}$
${log}_{10} a = b \Rightarrow a = 10^{b}$

Now, $10^{2 b - 3} = \frac{10^{2 b}}{10^{3}} = \frac{a^{2}}{10^{3}} = \frac{a^{2}}{1000}$

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