Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^-3 x 7^-5 as an expression with positive exponents only.(1 point)

Answer 1

To simplify the expression \( 7^{-3} \times 7^{-5} \) and rewrite it using only positive exponents, we can use the property of exponents that states:

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

We can combine the terms using the property of exponents that says \( a^m \times a^n = a^{m+n} \). Thus:

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

Now we apply the property of negative exponents:

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

Therefore, the expression equivalent to \( 7^{-3} \times 7^{-5} \) with positive exponents only is:

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