Question

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

Answer 1

To apply the Property of Negative Integer Exponents, we first recall that for any non-zero number \( a \) and a negative exponent \( n \), the expression can be rewritten as:

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

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

According to the property of exponents which states that \( a^m \cdot a^n = a^{m+n} \), we can combine the exponents since the bases are the same:

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

Next, we convert this into an expression with positive exponents:

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

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

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