Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅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 can use the property of multiplication of exponents:

a^m * a^n = a^(m+n).

So, applying this property to the expression 3^7 * 3^(-9), we can add the exponents:

3^(7+(-9)) = 3^(7-9) = 3^(-2).

To solve this expression, we can use the property of negative exponents:

a^(-n) = 1 / a^n.

Applying this property to 3^(-2), we get:

3^(-2) = 1 / 3^2 = 1 / 9.

Therefore, the solution to the expression 3^7 * 3^(-9) is 1/9.