%5E3.jpeg "(2x^2y^5)^3")
Simplifying (2x^2y^5)^3
This expression involves raising a product with exponents to another power. To simplify this, we can use the following properties of exponents:
- (ab)^n = a^n * b^n : When raising a product to a power, we raise each factor to that power.
- (a^m)^n = a^(m*n) : When raising a power to another power, we multiply the exponents.
Let's apply these properties step by step:
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Apply the first property: (2x^2y^5)^3 = 2^3 * (x^2)^3 * (y^5)^3
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Apply the second property: 2^3 * (x^2)^3 * (y^5)^3 = 2^3 * x^(23) * y^(53)
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Simplify the exponents: 2^3 * x^(23) * y^(53) = 8x^6y^15
Therefore, the simplified form of (2x^2y^5)^3 is 8x^6y^15.