-2%2F3.jpeg "(-64) 2/3")
Understanding (-64)<sup>2/3</sup>
The expression (-64)<sup>2/3</sup> might seem daunting at first, but it's actually a fairly straightforward calculation once you understand the properties of exponents and roots. Here's a breakdown:
Fractional Exponents
Fractional exponents represent a combination of powers and roots. The numerator of the fraction indicates the power, while the denominator indicates the root.
In this case, 2/3 means we need to find the cube root (3 in the denominator) of -64 and then square it (2 in the numerator).
Solving the Expression
- Cube Root: The cube root of -64 is -4 because -4 * -4 * -4 = -64.
- Square: Squaring -4 gives us (-4)<sup>2</sup> = 16.
Therefore, (-64)<sup>2/3</sup> = 16.
Key Points to Remember
- Negative Base: When dealing with a negative base and a fractional exponent where the denominator is odd (like in our case), the result will be negative.
- Fractional Exponents and Roots: Understanding the relationship between fractional exponents and roots is crucial for solving these types of expressions.
- Calculator: While the process is simple, calculators can be used to verify your calculations.
By breaking down the expression and understanding the properties of exponents and roots, you can confidently solve (-64)<sup>2/3</sup> and similar expressions.