Question

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

Remaining Attempts : 3

Answer 1

To apply the Property of Negative Integer Exponents, we use the rule that states \( a^{-m} = \frac{1}{a^m} \) and that when multiplying with the same base, we can add the exponents:

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

Thus, to simplify \( 7^{-3} \cdot 7^{-5} \):

1. First, add the exponents:

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

2. Then, apply the property of negative exponents:

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

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

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