Question

explain why (-64)1/3 equals -64 1/3 but (-64)1/2 does not equal -64 1/2

Answer 1

Answer:

1/3 would make it a repeating decimal so a fraction is prettier,

1/2 would make it a whole number: -64 * 1/2 = -32

Answer 2

The two expressions are equal because the presence of the negative sign does not affect the result

The first expression will give a complex number since we cannot find the square root of a negative number

Given the following surd functions $(-64)^{\frac{1}{3} } \ and \ (-64)^{\frac{1}{2} }$

We are to explain why they are not equal.

For the expression $(-64)^{\frac{1}{3} }$, this can also be written as $\sqrt[3]{-64}$ . The expression means that we need a value such that if the value is multiplied in 3 places will give -64. Hence:

$(-64)^{\frac{1}{3} }=-\sqrt[3]{-64} =-4\\-64^{\frac{1}{3} }=-\sqrt[3]{64} =-4$

The two expressions are equal because the presence of the negative sign does not affect the result

On the contrary;

$(-64)^{\frac{1}{2} }=\sqrt{-64} = 8i\\-64^{\frac{1}{2} }=-\sqrt{64} =-8$

These two expressions are NOT equal because the presence of the negative sign affects the result. The first expression will give a complex number since we cannot find the square root of a negative number

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