Question

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=

Answer 1

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

For the expression \( 7^{-3} \cdot 7^{-5} \), we first combine the exponents since they have the same base. The property for multiplying expressions with the same base states:

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

Applying this to our expression:

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

Now, to express \( 7^{-8} \) with positive exponents, we use the negative exponent rule:

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

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

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