%5E3.jpeg "(2y^5)^3")
Simplifying the Expression (2y^5)^3
This article explores the simplification of the expression (2y^5)^3. This expression involves raising a product of a constant and a variable to a power. We will leverage the rules of exponents to arrive at the simplified form.
Understanding the Rules of Exponents
Before diving into the simplification, let's recall the relevant rules of exponents:
- Product of powers: (a^m) * (a^n) = a^(m+n)
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Simplifying the Expression
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Apply the power of a product rule: (2y^5)^3 = 2^3 * (y^5)^3
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Apply the power of a power rule: 2^3 * (y^5)^3 = 8 * y^(5*3)
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Simplify the exponent: 8 * y^(5*3) = 8y^15
Therefore, the simplified form of (2y^5)^3 is 8y^15.
Conclusion
By applying the rules of exponents, we have successfully simplified the expression (2y^5)^3 to 8y^15. This demonstrates how understanding the properties of exponents enables us to efficiently manipulate and simplify expressions involving powers.