%5E2(2x%5E4y%5E3)%2F6x%5E8y.jpeg "(3xy)^2(2x^4y^3)/6x^8y")
Simplifying Algebraic Expressions: (3xy)^2(2x^4y^3)/6x^8y
In this article, we will learn how to simplify the algebraic expression (3xy)^2(2x^4y^3)/6x^8y. Simplifying algebraic expressions involves combining like terms, using the properties of exponents, and canceling out any common factors.
Step 1: Evaluate the Exponents
First, let's evaluate the exponents in the expression. We have (3xy)^2, which means we need to square the expression inside the parentheses. Using the power rule of exponents, we get:
(3xy)^2 = 3^2 × x^2 × y^2
= 9x^2y^2
Step 2: Multiply the Expressions
Next, we need to multiply the expressions (9x^2y^2) and (2x^4y^3). We can do this by multiplying the coefficients (numbers) and adding the exponents of the variables with the same base.
9x^2y^2 × 2x^4y^3
= 18x^(2+4)y^(2+3)
= 18x^6y^5
Step 3: Divide by the Common Factor
Now, we need to divide the expression by 6x^8y. To do this, we can rewrite the division as a fraction and cancel out any common factors.
18x^6y^5 / 6x^8y
= (18/6) × (x^6/x^8) × (y^5/y)
= 3 × x^(6-8) × y^(5-1)
= 3 × x^(-2) × y^4
= 3y^4/x^2
Therefore, the simplified form of the algebraic expression (3xy)^2(2x^4y^3)/6x^8y is 3y^4/x^2.
