%5E3%2F24x%5E-2y.jpeg "(2x^3y^-4)^3/24x^-2y")
Simplifying Expressions: (2x^3y^-4)^3/24x^-2y
In this article, we will explore how to simplify the expression (2x^3y^-4)^3/24x^-2y. To simplify this expression, we need to follow the order of operations and apply the rules of exponents.
Step 1: Simplify the Numerator
The numerator of the expression is (2x^3y^-4)^3. To simplify this, we can apply the rule of exponents that states (a^b)^c = a^(b*c). In this case, a = 2x^3y^-4, b = 3, and c = 3.
(2x^3y^-4)^3 = 2^(3*1) * x^(3*3) * y^(-4*3)
= 2^3 * x^9 * y^-12
= 8x^9y^-12
Step 2: Simplify the Denominator
The denominator of the expression is 24x^-2y. We can simplify this by rewriting 24 as 2^3 * 3 and applying the rule of exponents that states a^b * a^c = a^(b+c).
24x^-2y = 2^3 * 3 * x^-2 * y
= 2^3 * 3 * x^(-2) * y
Step 3: Divide the Numerator by the Denominator
Now, we can divide the numerator by the denominator to simplify the entire expression.
(8x^9y^-12) / (2^3 * 3 * x^(-2) * y)
= 8x^9y^-12 / (8 * x^-2 * y)
= x^(9-(-2)) * y^(-12-1)
= x^11y^-13
Therefore, the simplified expression is x^11y^-13.
