Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^-3 x 7^-5 with positive exponents only.

7^-3 x 7^-5 = {blank}

Answer 1

To simplify the expression \( 7^{-3} \times 7^{-5} \) using the property of negative integer exponents, we first use the rule that states:

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

Applying this rule:

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

Now, to express \( 7^{-8} \) with a positive exponent, we can use the property that states:

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

Thus,

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

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

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

So, filling in the blank:

\[
7^{-3} \times 7^{-5} = \frac{1}{7^8}
\]