(3xy)^2x^4y/x^5

3 min read Jun 16, 2024

Simplifying Algebraic Expressions: (3xy)^(2x^4y)/x^5

This article will guide you through simplifying the algebraic expression (3xy)^(2x^4y)/x^5. We'll break down the process step-by-step using the rules of exponents.

Understanding the Expression

Let's first analyze the expression:

(3xy)^(2x^4y): This represents a product of variables raised to an exponent.
x^5: This is a single variable raised to a power.

Applying the Rules of Exponents

To simplify this expression, we'll utilize the following rules:

(a^m)^n = a^(m*n): When raising a power to another power, we multiply the exponents.
(ab)^n = a^n * b^n: The power of a product is the product of the powers.
a^m / a^n = a^(m-n): When dividing powers with the same base, we subtract the exponents.

Simplifying the Expression

Let's apply these rules to our expression:

Simplify the numerator:
- (3xy)^(2x^4y) = 3^(2x^4y) * x^(2x^4y) * y^(2x^4y)
Combine the numerator and denominator:
- 3^(2x^4y) * x^(2x^4y) * y^(2x^4y) / x^5
Simplify the x terms:
- 3^(2x^4y) * x^(2x^4y - 5) * y^(2x^4y)

Final Simplified Expression

The simplified form of the expression (3xy)^(2x^4y)/x^5 is 3^(2x^4y) * x^(2x^4y - 5) * y^(2x^4y).

Conclusion

By using the fundamental rules of exponents, we successfully simplified the complex expression. This process highlights the importance of understanding these rules for manipulating and simplifying algebraic expressions.