(16xy^3/-24x^4y)^-3
simplify the rational expression in the form A/B. Single fraction with only positive exponents.
-27x^9/8y^6
To simplify the rational expression (16xy^3/-24x^4y)^-3, we need to follow these steps:
Step 1: Simplify the expression inside the parentheses.
Step 2: Divide the numerator and the denominator by their greatest common factor (GCF).
Step 3: Apply the negative exponent to flip the fraction.
Step 4: Simplify any remaining common factors.
Let's go through each step in detail:
Step 1: Simplify the expression inside the parentheses.
The expression inside the parentheses is (16xy^3/-24x^4y). To simplify it, first, let's simplify the constant values:
16 / -24 = -2/3
Now, let's simplify the variables:
x / x^4 = 1 / x^(4-1) = 1 / x^3
y^3 / y = y^(3-1) = y^2
The simplified expression inside the parentheses becomes: (-2/3) * (1 / x^3) * (y^2)
Step 2: Divide the numerator and the denominator by their greatest common factor (GCF).
The GCF between -2, 3, and x^3 is 1. Therefore, we divide the numerator and the denominator by 1, which does not change the value of the fraction. So the expression remains the same.
Step 3: Apply the negative exponent to flip the fraction.
Applying the negative exponent means flipping the fraction and changing the sign of the exponent:
((-2/3) * (1 / x^3) * (y^2))^-3 = (3/(-2)) * (x^3/1) * (y^-2)
Step 4: Simplify any remaining common factors.
The expression (3/(-2)) simplifies to -3/2.
The final simplified expression is: (-3/2) * (x^3) * (1/y^2)
So the rational expression (16xy^3/-24x^4y)^-3 simplifies to (-3/2) * (x^3) * (1/y^2) in the form A/B.