%5E5.jpeg "(-2ab^4)^5")
Simplifying (-2ab^4)^5
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (-2ab^4)^5.
Understanding the Properties
To simplify this expression, we need to understand a few key properties:
- Product of Powers: When raising a product to a power, we raise each factor to that power: (ab)^n = a^n b^n
- Power of a Power: When raising a power to another power, we multiply the exponents: (a^m)^n = a^(m*n)
- Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive exponent: a^(-n) = 1/a^n
Applying the Properties
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Apply the Product of Powers property: (-2ab^4)^5 = (-2)^5 * a^5 * (b^4)^5
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Apply the Power of a Power property: (-2)^5 * a^5 * (b^4)^5 = (-2)^5 * a^5 * b^(4*5)
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Simplify: (-2)^5 * a^5 * b^(4*5) = -32a^5b^20
Conclusion
Therefore, the simplified form of (-2ab^4)^5 is -32a^5b^20.