Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7 superscript −3⋅7 superscript −5
with positive exponents only.(1 point)
7 superscript −3⋅7 superscript −5=

Answer 1

To generate an expression equivalent to \( 7^{-3} \cdot 7^{-5} \) with positive exponents only, we can use the property of exponents that states:

\[
a^m \cdot a^n = a^{m+n}
\]

Applying this property, we have:

\[
7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8}
\]

Next, to convert the expression \( 7^{-8} \) to a positive exponent, we utilize the property of negative integer exponents:

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

Thus, we have:

\[
7^{-8} = \frac{1}{7^8}
\]

So, the expression \( 7^{-3} \cdot 7^{-5} \) with positive exponents is:

\[
\frac{1}{7^8}
\]