%5E3.jpeg "(6xy^5)^3")
Simplifying (6xy^5)^3
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves expressions raised to a power, such as (6xy^5)^3. Let's break down how to simplify this expression:
Understanding the Rules
The key rule we need is the power of a product rule:
(ab)^n = a^n * b^n
This rule states that when raising a product to a power, we raise each factor in the product to that power.
Applying the Rule
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Identify the factors: In our expression (6xy^5)^3, the factors are 6, x, and y^5.
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Apply the power rule: We raise each factor to the power of 3.
- 6^3 = 6 * 6 * 6 = 216
- x^3 = x^3
- (y^5)^3 = y^(5*3) = y^15
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Multiply the results: Now we multiply the simplified factors together.
- 216 * x^3 * y^15 = 216x^3y^15
Conclusion
Therefore, the simplified form of (6xy^5)^3 is 216x^3y^15.