%5E4.jpeg "(3ab^4)^4")
Simplifying (3ab^4)^4
In mathematics, simplifying expressions is a key skill. Let's explore how to simplify the expression (3ab^4)^4.
Understanding the Rules
To simplify this expression, we need to understand two key rules of exponents:
- Power of a Product: (xy)^n = x^n * y^n
- Power of a Power: (x^m)^n = x^(m*n)
Applying the Rules
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Apply the Power of a Product rule: (3ab^4)^4 = 3^4 * a^4 * (b^4)^4
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Apply the Power of a Power rule: 3^4 * a^4 * (b^4)^4 = 3^4 * a^4 * b^(4*4)
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Simplify the exponents: 3^4 * a^4 * b^(4*4) = 81a^4b^16
Final Result
Therefore, the simplified expression for (3ab^4)^4 is 81a^4b^16.