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

Answer 1

To apply the Property of Negative Integer Exponents, we can first combine the exponents of \(7^{-3} \cdot 7^{-5}\). According to the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), we can add the exponents:

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

Now, to convert \(7^{-8}\) into an expression with positive exponents, we use the property of negative exponents, which states that \(a^{-n} = \frac{1}{a^n}\):

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

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

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