%5E5(4xy%5E-3)%5E-7.jpeg "(12x^2y^-2)^5(4xy^-3)^-7")
Simplifying the Expression (12x^2y^-2)^5(4xy^-3)^-7
In this article, we will simplify the expression (12x^2y^-2)^5(4xy^-3)^-7. To simplify this expression, we will apply the rules of exponents and simplify the expression step by step.
Step 1: Expand the first part of the expression
(12x^2y^-2)^5 can be expanded as:
(12x^2y^-2)^5 = 12^5(x^2)^5(y^-2)^5
= 12^5x^10y^-10
Step 2: Expand the second part of the expression
(4xy^-3)^-7 can be expanded as:
(4xy^-3)^-7 = 4^-7(x^-7)(y^-3)^-7
= 4^-7x^-7y^21
Step 3: Multiply the two expanded expressions
Now, we multiply the two expanded expressions:
12^5x^10y^-10 * 4^-7x^-7y^21
Step 4: Simplify the expression
To simplify the expression, we can start by combining the like terms:
12^5 * 4^-7 = (12/4)^5 = 3^5
x^10 * x^-7 = x^3
y^-10 * y^21 = y^11
So, the simplified expression is:
(3^5)x^3y^11
= 243x^3y^11
Therefore, the simplified expression for (12x^2y^-2)^5(4xy^-3)^-7 is 243x^3y^11.
