%5E3.jpeg "(4x^4y^-4)^3")
Simplifying (4x^4y^-4)^3
In mathematics, simplifying expressions is a crucial skill. Let's explore how to simplify the expression (4x^4y^-4)^3.
Understanding the Rules
To tackle this problem, we need to recall a couple of key rules of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Rules
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Apply the power of a product rule: (4x^4y^-4)^3 = 4^3 * (x^4)^3 * (y^-4)^3
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Apply the power of a power rule: 4^3 * (x^4)^3 * (y^-4)^3 = 64 * x^(43) * y^(-43)
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Simplify: 64 * x^(43) * y^(-43) = 64x^12y^-12
Final Result
The simplified form of (4x^4y^-4)^3 is 64x^12y^-12. While this is a valid form, it's often preferred to express exponents with positive values. We can achieve this by using the following rule:
- Negative Exponent: a^-n = 1/a^n
Applying this rule to our simplified expression:
64x^12y^-12 = 64x^12 / y^12
Therefore, the fully simplified form of the expression is 64x^12 / y^12.