Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
37⋅3− exponet9?

Answer 1

To simplify the expression \( 37 \cdot 3^{-9} \) using properties of integer exponents, we can rewrite the term with the negative exponent. The property of exponents states that \( a^{-n} = \frac{1}{a^n} \).

So, we can rewrite \( 3^{-9} \) as:

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

Now substituting this back into the original expression:

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

This can be further simplified to:

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

Next, we need to calculate \( 3^9 \). We can find this value:

\[
3^9 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 19683
\]

Now we can substitute \( 3^9 \) back into the fraction:

\[
\frac{37}{3^9} = \frac{37}{19683}
\]

Thus, the simplified fraction with no remaining exponents is:

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

Therefore, the final answer is:

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