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

Question

7 raised to the −3 power⋅7 raised to the −5 power=

Answer 1

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

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

We also have the property of exponents that states when multiplying like bases, we can add their exponents:

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

Using these properties, let's simplify the expression:

1. Combine the exponents:

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

2. Now apply the property of negative exponents:

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

Thus, the expression \( 7^{-3} \cdot 7^{-5} \) can be rewritten as:

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

This is the equivalent expression with positive exponents only.