which expression is equivalent to (3a)^{-2}?\n\\(\\frac{1}{9a^{2}}\\)\n\\(\\frac{1}{3a^{2}}\\)\n\\(\\frac{3}{…

which expression is equivalent to (3a)^{-2}?\n\\(\\frac{1}{9a^{2}}\\)\n\\(\\frac{1}{3a^{2}}\\)\n\\(\\frac{3}{a^{2}}\\)\n\\(\\frac{9}{a^{2}}\\)

which expression is equivalent to (3a)^{-2}?\n\\(\\frac{1}{9a^{2}}\\)\n\\(\\frac{1}{3a^{2}}\\)\n\\(\\frac{3}{a^{2}}\\)\n\\(\\frac{9}{a^{2}}\\)

Answer

Explanation:

Step1: Apply negative - exponent rule

According to the rule (x^{-n}=\frac{1}{x^{n}}), for ((3a)^{-2}), we have ((3a)^{-2}=\frac{1}{(3a)^{2}}).

Step2: Expand ((3a)^{2})

Using the power - of - a - product rule ((xy)^{n}=x^{n}y^{n}), where (x = 3), (y=a) and (n = 2), we get ((3a)^{2}=3^{2}\times a^{2}=9a^{2}). So (\frac{1}{(3a)^{2}}=\frac{1}{9a^{2}}).

Answer:

A. (\frac{1}{9a^{2}})