%5E5.jpeg "(-3v)^5")
Simplifying (-3v)^5
In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves raising a product to a power. Let's take a look at how to simplify (-3v)^5.
Understanding the Rules
The key to simplifying this expression lies in understanding the following rules of exponents:
- Product to a power: (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 product to a power rule:
(-3v)^5 = (-3)^5 * v^5 -
Calculate (-3)^5: (-3)^5 = (-3) * (-3) * (-3) * (-3) * (-3) = -243
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Combine the results: (-3)^5 * v^5 = -243 * v^5 = -243v^5
Conclusion
Therefore, the simplified form of (-3v)^5 is -243v^5. This process highlights how understanding the rules of exponents allows us to efficiently simplify complex expressions.