Apply the property of negative integer exponents to generate an expression equivalent to seven -3 power times seven -5 power with positive exponents only

Answer 1

To apply the property of negative integer exponents and generate an equivalent expression with positive exponents, we can use the following rule:

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

Given the expression \( 7^{-3} \times 7^{-5} \), we first apply the property of exponents that states:

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

So, for our expression:

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

Now, we can express \( 7^{-8} \) using positive exponents:

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

Thus, the equivalent expression with positive exponents only is:

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