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

Answer 1

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

Starting with the expression:

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

We can convert the negative exponents to positive by applying the rule:

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

Substituting these into the original expression gives:

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

Thus, the expression \( 3^{-17} \cdot 8^{-14} \) is equivalent to:

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

This expression has only positive exponents.