2%2F3.jpeg "(-64)2/3")
Understanding (-64)<sup>2/3</sup>
The expression (-64)<sup>2/3</sup> might look intimidating at first, but it's actually quite straightforward to solve. Let's break it down step by step:
Fractional Exponents
Fractional exponents represent a combination of roots and powers. In this case, the exponent 2/3 means we need to take both a cube root (3 in the denominator) and a square (2 in the numerator).
Solving the Expression
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Cube root: Find the cube root of -64. This means finding a number that, when multiplied by itself three times, equals -64. The cube root of -64 is -4.
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Square: Now, square the result from step 1, meaning (-4) * (-4) = 16.
Therefore, (-64)<sup>2/3</sup> = 16.
Key Points
- Negative base: Even though the base is negative, the final result is positive. This is because the exponent is even.
- Order: The order of operations matters. You must first find the cube root, then square the result.
Understanding fractional exponents is crucial in various areas of mathematics, including algebra, calculus, and even physics. By breaking down complex expressions into simpler steps, you can tackle seemingly difficult problems with ease.