Question

Apply the Property of Negative Integer Exponents to generate and expression equivalent to 3 to the -17 over 8 to the -14 with positive exponents only.

Answer 1

To apply the property of negative integer exponents, we use the rule that states \( a^{-n} = \frac{1}{a^n} \).

We start with the expression:

\[
\frac{3^{-17}}{8^{-14}}
\]

Using the property of negative exponents, we can rewrite the expression:

\[
\frac{3^{-17}}{8^{-14}} = \frac{1}{3^{17}} \cdot \frac{8^{14}}{1} = \frac{8^{14}}{3^{17}}
\]

Thus, the equivalent expression with positive exponents only is:

\[
\frac{8^{14}}{3^{17}}
\]