Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14
3
−
17
8
−
14
with positive exponents only.(1 point)
3−178−14=
3
−
17
8
−
14
=

Answer 1

To convert the expression \( 3^{-17} 8^{-14} \) to one with positive exponents, we use the property of negative integer exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Applying this to the given expression:

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

Now, we can rewrite the entire expression:

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

Thus, the expression with positive exponents only is:

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