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 apply the properties of integer exponents to generate equivalent expressions, we can use the property that for any positive integer a, a^(-n) = 1/a^n.

So, for the expression 3^7 • 3^(-9), we can rewrite it as 3^7 • 1/3^9.

Now, using the property of exponentiation that a^m • a^n = a^(m+n), we can simplify the expression further:

3^7 • 1/3^9 = 3^(7+(-9)) = 3^(-2) = 1/3^2 = 1/9.

Therefore, the simplified fraction is 1/9.