%5E3.jpeg "(2x^5y)^3")
Simplifying (2x^5y)^3
This expression involves raising a monomial to a power. To simplify it, we can use the following rules of exponents:
- (a^m)^n = a^(m*n) - This rule tells us that when raising a power to another power, we multiply the exponents.
- (ab)^n = a^n * b^n - This rule states that when raising a product to a power, we raise each factor to that power.
Let's apply these rules to our expression:
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Distribute the exponent: (2x^5y)^3 = 2^3 * (x^5)^3 * y^3
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Simplify each term: 2^3 * (x^5)^3 * y^3 = 8 * x^(5*3) * y^3
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Combine the exponents: 8 * x^(5*3) * y^3 = 8x^15y^3
Therefore, the simplified form of (2x^5y)^3 is 8x^15y^3.