(3x^4y^3)^4 Times 2(y^2)^3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (3x^4y^3)^4 times 2(y^2)^3

This problem involves simplifying an expression with exponents. Let's break it down step-by-step:

Understanding the Rules of Exponents

• Product of Powers: When multiplying powers with the same base, you add the exponents. For example, x^m * x^n = x^(m+n)
• Power of a Power: When raising a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n)
• Power of a Product: When raising a product to a power, you raise each factor to that power. For example, (x*y)^n = x^n * y^n

Simplifying the Expression

1. Simplify the first term (3x^4y^3)^4:

   • Apply the power of a product rule: (3x^4y^3)^4 = 3^4 * (x^4)^4 * (y^3)^4
   • Apply the power of a power rule: 3^4 * (x^4)^4 * (y^3)^4 = 81x^16y^12

2. Simplify the second term 2(y^2)^3:

   • Apply the power of a power rule: 2(y^2)^3 = 2y^6

3. Multiply the simplified terms:

   • 81x^16y^12 * 2y^6 = 162x^16y^18

Final Answer

The simplified expression is 162x^16y^18.