%5E4.jpeg "(2x^4y^4)^4")
Simplifying the Expression (2x^4y^4)^4
This article will break down the simplification process of the expression (2x^4y^4)^4. We'll explore the fundamental concepts of exponents and how they apply to this specific example.
Understanding Exponents
Exponents represent repeated multiplication. For example, x^n means 'x multiplied by itself n times'. So, x^4 would be xxx*x.
Applying the Exponent Rule
A key rule in simplifying expressions with exponents is: (a^m)^n = a^(m*n). This rule states that when raising a power to another power, you multiply the exponents.
Simplifying the Expression
Let's apply this rule to our expression (2x^4y^4)^4:
- Apply the rule to the entire expression: (2x^4y^4)^4 = 2^(41) * x^(44) * y^(4*4)
- Simplify the exponents: 2^4 * x^16 * y^16
- Calculate 2^4: 16 * x^16 * y^16
Therefore, the simplified form of (2x^4y^4)^4 is 16x^16y^16.
Summary
This simplification demonstrates the power of exponent rules and how they allow us to efficiently manipulate expressions involving repeated multiplication. Understanding these rules is crucial for working with polynomial expressions and other mathematical concepts.