Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9

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 \( 37 \cdot 3^{-9} \) using the Properties of Integer Exponents, we can rewrite \( 3^{-9} \) as \( \frac{1}{3^9} \). This gives us:

\[ 37 \cdot 3^{-9} = 37 \cdot \frac{1}{3^9} \]

Next, we can rewrite this as:

\[ \frac{37}{3^9} \]

Now, we need to compute \( 3^9 \):

\[ 3^9 = 19683 \]

So, we can rewrite the expression as:

\[ \frac{37}{19683} \]

Thus, the final answer to the expression, simplified as a fraction with no remaining exponents, is:

\[ \frac{37}{19683} \]