(4x^2y^5)^4

2 min read Jun 16, 2024
(4x^2y^5)^4

Simplifying Expressions with Exponents: (4x²y⁵)⁴

This article delves into the simplification of the expression (4x²y⁵)⁴. Understanding the rules of exponents is crucial for efficiently manipulating and solving algebraic expressions.

The Power of a Product Rule

The key to simplifying this expression lies in the power of a product rule:

(ab)ⁿ = aⁿbⁿ

This rule states that when raising a product to a power, you can distribute the power to each factor within the product.

Applying the Rule

Let's apply this rule to our expression:

(4x²y⁵)⁴ = 4⁴ (x²)⁴ (y⁵)⁴

Now, we need to apply another rule:

(aⁿ)ᵐ = aⁿᵐ

This rule states that when raising a power to another power, we multiply the exponents.

Final Simplification

Applying this rule to our expression, we get:

4⁴ (x²)⁴ (y⁵)⁴ = 256x⁸y²⁰

Therefore, the simplified form of (4x²y⁵)⁴ is 256x⁸y²⁰.

Summary

By applying the power of a product rule and the rule for raising a power to another power, we successfully simplified the expression (4x²y⁵)⁴ to 256x⁸y²⁰. This process demonstrates the importance of understanding exponent rules for simplifying complex algebraic expressions.

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