%5E4.jpeg "(2x^-2y^3/3xy^-4)^4")
Simplifying Algebraic Expressions: (2x^-2y^3/3xy^-4)^4
In this article, we will explore how to simplify the algebraic expression (2x^-2y^3/3xy^-4)^4. This expression may look intimidating, but with the right steps and techniques, we can simplify it to a more manageable form.
Step 1: Simplify the expression inside the parentheses
Before we can simplify the entire expression, we need to simplify the expression inside the parentheses. We can start by rewriting the expression as:
(2/x^2 \* y^3) / (3x \* y^-4)
Next, we can simplify the numerator and denominator separately:
Numerator: 2/x^2 \* y^3 = 2y^3 / x^2
Denominator: 3x \* y^-4 = 3x / y^4
Now, we can rewrite the entire expression as:
(2y^3 / x^2) / (3x / y^4)
Step 2: Simplify the fraction
To simplify the fraction, we can cancel out any common factors between the numerator and denominator. In this case, we can cancel out the y terms:
(2y^3 / x^2) / (3x / y^4) = (2y^3/y^4) / (3x / x^2)
This simplifies to:
(2/y) / (3/x)
Step 3: Simplify the expression further
Now, we can simplify the expression further by canceling out any common factors between the numerator and denominator:
(2/y) / (3/x) = 2x / 3y
Step 4: Raise the simplified expression to the power of 4
Finally, we need to raise the simplified expression to the power of 4:
(2x / 3y)^4
This expression can be expanded using the rules of exponents:
(2x / 3y)^4 = 2^4 \* x^4 / 3^4 \* y^4
Simplifying further, we get:
(2x / 3y)^4 = 16x^4 / 81y^4
And that's the final simplified form of the expression (2x^-2y^3/3xy^-4)^4!
Conclusion
Simplifying algebraic expressions can be a challenging task, but with the right steps and techniques, we can simplify even the most complex expressions. In this article, we learned how to simplify the expression (2x^-2y^3/3xy^-4)^4 by breaking it down into smaller steps and using the rules of exponents to simplify the expression.
