%5E3.jpeg "(2xy^5)^3")
Simplifying (2xy^5)^3
In mathematics, simplifying expressions is a key skill. Let's break down how to simplify the expression (2xy^5)^3.
Understanding the Rules
The key to this simplification lies in the power of a product and the power of a power rules.
- Power of a product: (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 power of a product rule: (2xy^5)^3 = 2^3 * x^3 * (y^5)^3
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Apply the power of a power rule: 2^3 * x^3 * (y^5)^3 = 2^3 * x^3 * y^(5*3)
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Simplify the exponents: 2^3 * x^3 * y^(5*3) = 8x^3y^15
The Final Result
Therefore, the simplified form of (2xy^5)^3 is 8x^3y^15.