Applying the Power Rule of Exponents, what is the exponent in an equivalent form of ((1/6)^3)^3%0D%0A(%0D%0A(%0D%0A1%0D%0A6%0D%0A)%0D%0A3%0D%0A)%0D%0A3%0D%0A? Answer with a whole number for the exponent where the base is 1/6%0D%0A1%0D%0A6%0D%0A.(1 point)

Answer 1

To simplify \(((\frac{1}{6})^3)^3\) using the Power Rule of Exponents, we can apply the rule that states \((a^m)^n = a^{m \cdot n}\).

Here, \(a = \frac{1}{6}\), \(m = 3\), and \(n = 3\).

So, we have:

\[ ((\frac{1}{6})^3)^3 = (\frac{1}{6})^{3 \cdot 3} = (\frac{1}{6})^{9} \]

Thus, the exponent in the equivalent form is 9.