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

Question

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 \( a^{-n} = \frac{1}{a^n} \).

Let's start with the expression:

\[ 7^{-3} \cdot 7^{-5} \]

According to the properties of exponents, when multiplying powers with the same base, we can add the exponents:

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

Now, we apply the property of negative exponents:

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

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

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

So, the equivalent expression with positive exponents only is:

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