Apply the properties of integer exponents to generate equivalent expressions to 3^7 x 3^-9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents
To generate equivalent expressions with only positive exponents, we can use the property that states:
\(a^{-b} = \frac{1}{a^b}\)
Applying this property to the expression \(3^7 \cdot 3^{-9}\), we can rewrite it as:
\(3^7 \cdot \frac{1}{3^9}\)
Next, we can use the property that states:
\(a^m \cdot a^n = a^{m+n}\)
Applying this property to the expression \(3^7 \cdot \frac{1}{3^9}\), we can simplify it as:
\(3^{7+(-9)} = 3^{-2}\)
Finally, using the property \(a^{-b} = \frac{1}{a^b}\), we can rewrite \(3^{-2}\) as:
\(\frac{1}{3^2} = \frac{1}{9}\)
Therefore, the solution to the expression \(3^7 \cdot 3^{-9}\) is \(\frac{1}{9}\).