(-2a)^4/3

Jasonbradley

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Jun 16, 2024

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Simplifying (-2a)^4/3

In mathematics, simplifying expressions often involves understanding the rules of exponents. The expression (-2a)^4/3 is an example of an expression involving fractional exponents. Here's how we can simplify it:

Understanding Fractional Exponents

A fractional exponent like 4/3 represents both a power and a root. The numerator (4) indicates the power to which the base is raised, while the denominator (3) indicates the root to be taken. In this case, 4/3 means "raise to the power of 4 and then take the cube root".

Applying the Rules

1. Distribute the exponent: When raising a product to a power, we distribute the exponent to each factor.

   • (-2a)^4/3 = (-2)^4/3 * (a)^4/3

2. Simplify each factor:

   • (-2)^4/3 = (-2)^4 * (-2)^(-1) (using the rule x^(m/n) = x^m * x^(-n))
   • (a)^4/3 = (a)^4 * (a)^(-1)

3. Calculate the powers:

   • (-2)^4 = 16
   • (a)^4 = a^4

4. Take the cube root:

   • 16^(1/3) = 2.52 (approximately)
   • (a^4)^(1/3) = a^(4/3)

Final Result

Therefore, the simplified form of (-2a)^4/3 is approximately 2.52a^(4/3).

Note: The result for the cube root of 16 is an approximation. It can be expressed more precisely using radical notation as 2√2.