use 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 that states:

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

Applying this property to the given expression, we have:

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

Exponents are the expressions that simplify to 0 can be removed, according to the property:

a^0 = 1 (except for a = 0).

Therefore:

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

To simplify a negative exponent, we use the property:

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

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

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

Finally, solving 1 / 3^2:

1 / 3^2 = 1 / 9.

Thus, the expression 3^7 * 3^(-9) is equivalent to 1/9 when simplified with no remaining exponents.