(4a^3/2b^4)^2

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (4a^3/2b^4)^2

This article will guide you through simplifying the expression (4a^3/2b^4)^2. We will use the rules of exponents and fractions to break down the problem step-by-step.

Understanding the Rules

Before we begin, let's recall some essential rules:

• Power of a Quotient: (a/b)^n = a^n/b^n
• Power of a Product: (ab)^n = a^n * b^n
• Power of a Power: (a^m)^n = a^(m*n)

Simplifying the Expression

1. Apply the Power of a Quotient rule:

   (4a^3/2b^4)^2 = (4a^3)^2 / (2b^4)^2

2. Apply the Power of a Product rule to the numerator and denominator:

   (4a^3)^2 / (2b^4)^2 = (4^2 * (a^3)^2) / (2^2 * (b^4)^2)

3. Apply the Power of a Power rule to the variables:

   (4^2 * (a^3)^2) / (2^2 * (b^4)^2) = 16a^6 / 4b^8

4. Simplify the numerical coefficients:

   16a^6 / 4b^8 = 4a^6 / b^8

Final Result

Therefore, the simplified form of the expression (4a^3/2b^4)^2 is 4a^6 / b^8.