Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(3^2x^3y/y^3)^−1
To simplify the expression (3^2x^3y/y^3)^−1, we can start by applying the negative exponent property, which states that a^(-n) = 1/a^n.
So, (3^2x^3y/y^3)^−1 can be rewritten as 1/(3^2x^3y/y^3).
Now, let's simplify the expression inside the parentheses:
3^2 = 9
x^3/x^3 = 1 (since x^3/x^3 is the same as x^(3-3) which equals x^0, and any non-zero number raised to the power of 0 is equal to 1)
y^1/y^3 = 1/y^(3-1) = 1/y^2
So, the expression (3^2x^3y/y^3) can be simplified to (9xy/y^2).
Now, let's go back to our original expression:
1/(3^2x^3y/y^3) = 1/(9xy/y^2).
To simplify this expression further, we can apply the reciprocal property, which states that 1/(a/b) = b/a.
So, our expression simplifies to (y^2)/(9xy).
Therefore, the simplified expression is (y^2)/(9xy).