%5E3.jpeg "(-3ab^2/4bc^4)^3")
Simplifying the Expression (-3ab^2/4bc^4)^3
This article will guide you through simplifying the expression (-3ab^2/4bc^4)^3. We will break down the process step-by-step, making it easy to understand.
Understanding the Rules
Before we start simplifying, let's recall some important rules of exponents:
- (a/b)^n = a^n/b^n: This rule applies when raising a fraction to a power.
- (a^m)^n = a^(m*n): This rule applies when raising a power to another power.
Step-by-Step Simplification
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Applying the first rule: We begin by applying the rule for raising a fraction to a power:
(-3ab^2/4bc^4)^3 = (-3ab^2)^3 / (4bc^4)^3
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Applying the second rule: Next, we apply the rule for raising a power to another power to both the numerator and denominator:
(-3ab^2)^3 / (4bc^4)^3 = (-3)^3 * (a)^3 * (b^2)^3 / (4)^3 * (b)^3 * (c^4)^3
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Simplifying: Now, we simplify the expression:
(-3)^3 * (a)^3 * (b^2)^3 / (4)^3 * (b)^3 * (c^4)^3 = -27a^3b^6 / 64b^3c^12
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Combining like terms: Finally, we combine the like terms by subtracting the exponents in the denominator from the exponents in the numerator:
-27a^3b^6 / 64b^3c^12 = -27a^3b^3 / 64c^12
Conclusion
Therefore, the simplified form of the expression (-3ab^2/4bc^4)^3 is -27a^3b^3 / 64c^12.