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Evaluating (-64)^4/3
In mathematics, evaluating expressions with fractional exponents can be tricky, but there's a simple approach. Here's how to break down the evaluation of (-64)^4/3.
Understanding Fractional Exponents
A fractional exponent like 4/3 indicates both a power and a root. The numerator (4) represents the power we raise the base to, and the denominator (3) represents the root we take.
In this case, (-64)^4/3 means:
- Cube root: Find the cube root of -64, which is -4 (since -4 * -4 * -4 = -64).
- Fourth power: Raise the result (-4) to the fourth power, which is (-4) * (-4) * (-4) * (-4) = 256.
Calculation
Therefore, (-64)^4/3 = 256.
Key Points
- Negative bases: When dealing with negative bases and fractional exponents, remember to consider the root. An odd root of a negative number is negative, while an even root is not defined in the real number system.
- Simplifying: Sometimes, you can simplify the expression before evaluating it. For example, if the base and the denominator of the exponent share a common factor, you can simplify it.
By following these steps, you can confidently evaluate expressions with fractional exponents.