The correct option is A 1 81Given, nbsp;(1 3 )^2 × 3^ 2 nbsp;= (1 3)^2× nbsp; nbsp;(1 3)^2 [a^ m = 1 a^m] nbsp;= (1 3)^2+2 [a^m × a^n = a ...

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Product Law of Exponent

Simplify, 1/3...

Question

Simplify, $(\frac{1}{3})^{2} \times 3^{- 2}$

\frac{1}{81}

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\frac{1}{27}

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27

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81

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Solution

The correct option is A $\frac{1}{81}$
Given, $(\frac{1}{3})^{2} \times 3^{- 2} = (\frac{1}{3})^{2} \times (\frac{1}{3})^{2} [a^{- m} = \frac{1}{a^{m}}] = (\frac{1}{3})^{2 + 2} [a^{m} \times a^{n} = a^{m + n}] = (\frac{1}{3})^{4} = \frac{1}{3^{4}} = \frac{1}{3 \times 3 \times 3 \times 3} = \frac{1}{81}$

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