Question

Apply the property of negative integer exponents to generate an expression equivalent to three minus power of 17/8 negative power of 14 with positive exponents only what is the answer?

Answer 1

To rewrite the expression \(3 - \left(\frac{17}{8}\right)^{-14}\) using only positive exponents, we first need to focus on the term with the negative exponent.

The property of negative exponents states that:

\[
a^{-n} = \frac{1}{a^n}
\]

Applying this to \(\left(\frac{17}{8}\right)^{-14}\):

\[
\left(\frac{17}{8}\right)^{-14} = \frac{1}{\left(\frac{17}{8}\right)^{14}}
\]

Therefore, the expression \(3 - \left(\frac{17}{8}\right)^{-14}\) can be rewritten as:

\[
3 - \frac{1}{\left(\frac{17}{8}\right)^{14}}
\]

Next, we can calculate \(\left(\frac{17}{8}\right)^{14}\):

\[
\left(\frac{17}{8}\right)^{14} = \frac{17^{14}}{8^{14}}
\]

This means the expression can further be rewritten as:

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

Overall, the expression \(3 - \left(\frac{17}{8}\right)^{-14}\) with all positive exponents can be expressed as:

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

This is the final expression with positive exponents only.