Question

Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7x3^-9 with only positive exponents, then solve the expression. Your answer will be simplified fraction with no remaining exponents.

Answer 1

To generate an equivalent expression with only positive exponents, we can use the property of adding exponents when multiplying bases with the same exponent.

Using this property, we have:
3^7 * 3^(-9) = 3^(7 + (-9))

Next, simplifying the exponent:
3^(7 + (-9)) = 3^(-2)

To solve the expression, we can write 3^(-2) as a fraction with the base raised to a positive exponent in the denominator:
3^(-2) = 1/3^2

Simplifying the fraction:
1/3^2 = 1/9

Therefore, the simplified fraction without remaining exponents is 1/9.