Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 3
7 ⋅ 3 −9
with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
3 7 ⋅ 3 −9=

Answer 1

To simplify the expression \( 3^7 \cdot 3^{-9} \) using the properties of integer exponents, we can use the property that states:

\[
a^m \cdot a^n = a^{m+n}
\]

In this case, we have:

\[
3^7 \cdot 3^{-9} = 3^{7 + (-9)} = 3^{7 - 9} = 3^{-2}
\]

Next, we can convert the negative exponent to a positive exponent by using the property:

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

Thus, we have:

\[
3^{-2} = \frac{1}{3^2}
\]

Now, calculating \( 3^2 \):

\[
3^2 = 9
\]

This gives us:

\[
3^{-2} = \frac{1}{9}
\]

Therefore, the final simplified expression for \( 3^7 \cdot 3^{-9} \) with only positive exponents is

\[
\frac{1}{9}
\]