To generate equivalent expressions with only positive exponents, we use the properties of integer exponents.
First, let's rewrite the expression 4^-9 as (1/4)^9. This is because any non-zero number raised to the power of -n is equivalent to 1 divided by the same number raised to the power of n.
Now, let's simplify the expression using the properties of exponents:
3^7 • 4^-9 = (3^7)(1/4^9)
Since both 3 and 4 are prime numbers, we cannot simplify any further using the properties of exponents.
To solve the expression, we can evaluate the powers of 3 and 4:
(3^7)(1/4^9) = 2187(1/262144)
Now, let's simplify this fraction. The numerator, 2187, and the denominator, 262144, have no common factors other than 1. Therefore, the fraction is already simplified.
Therefore, the simplified fraction is:
2187/262144