4.jpeg "(3x2y4)4")
Simplifying (3x^2y^4)^4
This expression involves several key concepts in algebra: exponents, the power of a product, and the power of a power. Let's break it down step by step.
Understanding the Terms
- (3x^2y^4): This represents a product of three terms: a constant (3), a variable with an exponent (x^2), and another variable with an exponent (y^4).
- ^4: This is the exponent applied to the entire expression within the parentheses. It means we multiply the expression by itself four times.
Applying the Rules
1. Power of a Product: When raising a product to a power, we raise each individual factor to that power.
Therefore, (3x^2y^4)^4 = 3^4 * (x^2)^4 * (y^4)^4
2. Power of a Power: When raising a power to another power, we multiply the exponents.
Applying this rule, we get: 3^4 * (x^2)^4 * (y^4)^4 = 81 * x^8 * y^16
Final Answer
The simplified form of (3x^2y^4)^4 is 81x^8y^16.