Question

apply the property of negative intenger exponents to generate an expression equivalent to 3 to the power of -17 over 8 to the power of -14 with positive exponents only.
enter ur answe as a fraction in simplest form

Answer 1

To simplify the expression \(\frac{3^{-17}}{8^{-14}}\) and express it with positive exponents only, we can use the property of negative integer exponents, which states that \(a^{-n} = \frac{1}{a^{n}}\).

Applying this property:

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

Dividing by a fraction is equivalent to multiplying by its reciprocal:

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

Next, we leave the expression as it is in terms of positive exponents:

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

Now we should check if this can be simplified. However, \(8^{14}\) and \(3^{17}\) have no common factors, so the expression is already in its simplest form.

Thus, the final answer is:

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