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)
To generate an equivalent expression with only positive exponents, we can rewrite $37\cdot3^{-9}$ as $\dfrac{37}{3^9}$.
To solve the expression, we can simplify the fraction. Notice that $3^9$ can be written as $3\times3\times3\times3\times3\times3\times3\times3\times3$. So, we have $$\dfrac{37}{3^9} = \dfrac{37}{3\times3\times3\times3\times3\times3\times3\times3\times3}.$$ Canceling out as many 3's as possible, we get $$\dfrac{37}{3\times3\times3\times3\times3\times3\times3\times3\times3} = \dfrac{37}{3^{9-3}} = \dfrac{37}{3^6}.$$
Therefore, the simplified expression is $\dfrac{37}{3^6}$.