Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17 x 8^−14 with positive exponents only.

Answer 1

To rewrite the expression \( 3^{-17} \times 8^{-14} \) using only positive exponents, we can apply the property of negative integer exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the original expression:

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

We can rewrite each term with positive exponents:

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

Now substituting these into the expression gives:

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

This can be combined into a single fraction:

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

Thus, the expression \( 3^{-17} \times 8^{-14} \) can be rewritten as:

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

This is the equivalent expression with positive exponents only.