Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5

Question

with positive exponents only.(1 point)

Answer 1

To apply the property of negative integer exponents, we can use the rule that states:

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

First, let's rewrite the expression \(7^{-3} \cdot 7^{-5}\).

Using the property of exponents, we can first combine the bases since they are the same:

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

Now, to express \(7^{-8}\) with positive exponents, we apply the property of negative exponents:

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

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

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