Apply the Properties of Integer Exponents to generate equivalent expressions to 3 superscript7⋅3− superscript9

Question

with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
37⋅3−9=

Answer 1

To simplify the expression \( 3^7 \cdot 3^{-9} \) using the properties of integer exponents, we can apply the rule that states \( a^m \cdot a^n = a^{m+n} \).

Here, we have: \[ 3^7 \cdot 3^{-9} = 3^{7 + (-9)} = 3^{7 - 9} = 3^{-2} \]

Next, to express this with only positive exponents, we can rewrite \( 3^{-2} \) as: \[ 3^{-2} = \frac{1}{3^2} \]

Now we can simplify \( \frac{1}{3^2} \): \[ \frac{1}{3^2} = \frac{1}{9} \]

Thus, the final answer is: \[ \frac{1}{9} \]