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.

Answer 1

To generate equivalent expressions with only positive exponents, we need to use the properties of integer exponents.

The expression is 37⋅3−9.

First, we can rewrite 37 as 3^7 since 37 is the same as 3 multiplied by itself 7 times.

Now, using the property a^m⋅a^n = a^(m+n), we can rewrite the expression as 3^7⋅3^-9.

Next, using the property a^m/a^n = a^(m-n), we can simplify the expression further:

3^7⋅3^-9 = 3^(7-9) = 3^-2.

Finally, using the property a^-n = 1/a^n, we can rewrite the expression as 1/3^2 = 1/9.

So, the expression 37⋅3^-9 is equivalent to 1/9.

Answer 2

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Answer 3

Apply the properties of integer exponents to generate equivalent expressions to 2^2/2^-4 with only positive exponents, then solve the expression. Provide the solution as a whole number.