%5E2%2F3.jpeg "(-64)^2/3")
Understanding (-64)^(2/3)
The expression (-64)^(2/3) involves both a negative base and a fractional exponent. Let's break down how to solve it:
Fractional Exponents
A fractional exponent like 2/3 represents both a root and a power. The denominator (3) indicates the cube root, while the numerator (2) indicates the square.
Therefore, (-64)^(2/3) can be rewritten as:
(Cube root of -64) squared
Calculating the Expression
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Cube root of -64: The cube root of -64 is -4 because (-4) * (-4) * (-4) = -64.
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Squaring the result: Squaring -4 gives us (-4)^2 = 16.
Therefore, (-64)^(2/3) = 16.
Key Points
- Negative bases: When dealing with negative bases and fractional exponents, the odd root of a negative number is negative.
- Order of operations: Always calculate the root before applying the power when dealing with fractional exponents.
By understanding these concepts, we can successfully evaluate expressions involving negative bases and fractional exponents.