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=
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.
To generate an equivalent expression with only positive exponents, we can apply the property of integer exponents, which states that when multiplying two numbers with the same base, we can add their exponents.
Using this property, we can simplify the expression as follows:
3^7⋅3^−9 = 3^(7 + (-9))
Now, let's simplify the exponent by adding the numbers:
3^(7 + (-9)) = 3^(-2)
The final expression is 3^(-2).