Question

Negative Integer Exponents Practice
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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 rewrite the expression \(7^{-3} \cdot 7^{-5}\) with positive exponents only, you can use the property of exponents that states:

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

Applying that property here:

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

Now, to convert \(7^{-8}\) into an expression with positive exponents, you use the property that states:

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

So,

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

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

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