Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(4x^2)(5x^−1)^2/(6y^3)(2y^−2)
To simplify the expression, we can apply the properties of exponents:
First, let's simplify the numerator: (5x^(-1))^2 = 5^2 * x^(-1 * 2) = 25x^(-2).
Now, let's simplify the denominator: (2y^(-2)) = 2 * y^(-2).
Putting it all together, the expression becomes:
(4x^2 * 25x^(-2)) / (6y^3 * 2 * y^(-2))
Now, let's simplify further by using the properties of multiplication and division:
(4 * 25 * x^2 * x^(-2)) / (6 * 2 * y^3 * y^(-2))
= (100 * x^(2-2)) / (12 * y^(3-2))
= 100 / 12 * x^(0) / y^(1)
= 8.3333 * x^0 * y^(-1)
Since x^0 is equal to 1, the expression further simplifies to:
8.3333 * (1) * y^(-1)
= 8.3333 / y^1
= 8.3333 / y