Using the properties of integer exponents, we can add the exponents when multiplying powers with the same base. Therefore, 3^7⋅3^−9 can be written as 3^(7 + (-9)).
Simplifying the exponent, 7 + (-9) = -2.
Therefore, 3^7⋅3^−9 is equivalent to 3^(-2).
To solve this expression with only positive exponents, we can use the property that a negative exponent is equal to the reciprocal of the base with a positive exponent.
Thus, 3^(-2) is equal to 1/(3^2).
Simplifying 1/(3^2), we get 1/9 as the final answer.
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.(1 point)
3^7⋅3^−9=
1 answer