Which is equivalent to the expression shown below? 3^2cdot 3^-2 A -3 B -1 C (1)/(769) D (1)/(3)

Question

Question

Which is equivalent to the expression shown below? 3^2cdot 3^-2 A -3 B -1 C (1)/(769) D (1)/(3)

Answer 1

The given expression is \[3^{2} \cdot 3^{-7}\]. In such arithmetic computations involving the same base but different exponents, the rule is to add the exponents when the bases are being multiplied together. In our case, the base of each numerical expression is the same. Therefore, adding the exponents together of 2 and -7 gives -5. This gives us \[3^{-5}\]. On further solving this, we sees that \[3^{-5}\] can be written as \[\frac{1}{3^{5}} \], equivalently, \[\frac{1}{243}\]. However, none of the options given in the question hold the right answer - there seems to be an error in the provided answer choices in the question. The correct answer of \(\frac{1}{243}\) was not listed.

Question

Which is equivalent to the expression shown below? 3^2cdot 3^-2 A -3 B -1 C (1)/(769) D (1)/(3)

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