Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(3xy2)−2
To simplify the expression, we can apply the property of exponents that states:
(x^m)^n = x^(m * n)
Using this property, we can rewrite the expression:
(3xy^2)^(-2) = 3^(-2) * (x^(-2)) * (y^2)^(-2)
Next, we simplify the numerical portion:
3^(-2) = (1/3)^2 = 1/9
Then, we simplify the y term with a negative exponent:
(y^2)^(-2) = y^(2 * -2) = y^(-4) = 1/y^4
Finally, we can rewrite the expression:
(3xy^2)^(-2) = 1/9 * (x^(-2)) * (1/y^4)
Therefore, the simplified expression is 1/9 * (1/x^2) * (1/y^4), or (1/9)(1/x^2)(1/y^4).