%5E4(x%5E3y%5E2)%5E-2.jpeg "(x^3y^5)^4(x^3y^2)^-2")
(x^3y^5)^4(x^3y^2)^-2: Simplify the Expression
In this article, we will simplify the expression (x^3y^5)^4(x^3y^2)^-2. To do this, we will use the laws of exponents and some algebraic manipulations.
Step 1: Expand the Exponents
First, let's expand the exponents using the power of a power rule, which states that (a^m)^n = a^(m*n). Applying this rule to the first part of the expression, we get:
(x^3y^5)^4 = x^(3*4)y^(5*4) = x^12y^20
Next, let's expand the exponents in the second part of the expression:
(x^3y^2)^-2 = x^(3*(-2))y^(2*(-2)) = x^-6y^-4
Step 2: Simplify the Expression
Now, we can simplify the expression by multiplying the two parts together:
x^12y^20 * x^-6y^-4 = x^(12-6)y^(20-4) = x^6y^16
Final Answer
The simplified expression is:
(x^3y^5)^4(x^3y^2)^-2 = x^6y^16
In conclusion, we have successfully simplified the given expression using the laws of exponents and some basic algebraic manipulations.
