(3/2b^4)^3

Jasonbradley

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Jun 16, 2024

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Simplifying (3/2b^4)^3

This article will walk you through simplifying the expression (3/2b^4)^3.

Understanding the Properties

To simplify this expression, we need to utilize a couple of key properties of exponents:

1. Power of a Product: (ab)^n = a^n * b^n
2. Power of a Quotient: (a/b)^n = a^n / b^n
3. Power of a Power: (a^m)^n = a^(m*n)

Applying the Properties

Let's break down the simplification step by step:

1. Apply the Power of a Quotient: (3/2b^4)^3 = 3^3 / (2b^4)^3

2. Apply the Power of a Product: 3^3 / (2b^4)^3 = 3^3 / (2^3 * (b^4)^3)

3. Apply the Power of a Power: 3^3 / (2^3 * (b^4)^3) = 3^3 / (2^3 * b^(4*3))

4. Simplify: 3^3 / (2^3 * b^(4*3)) = 27 / 8b^12

Final Answer

Therefore, the simplified form of (3/2b^4)^3 is 27/8b^12.