How do you simplify -4^(5/2)?

Apr 1, 2015

$- {4}^{\frac{5}{2}}$ is the same as $0 - {4}^{\frac{5}{2}}$. The exponent applies only to the $4$, not to the minus sign.

$- {4}^{\frac{5}{2}} = - \left({4}^{\frac{5}{2}}\right) = - \left({\sqrt[2]{4}}^{5}\right) = - \left({2}^{5}\right) = - \left(32\right) = - 32$

Perhaps I should add, regarding the negative sign:

$- {3}^{2}$ does not mean "the square of negative 3" It means "the negative of the square of 3.#

Mathematics is harder to speak than it is to write. Spoken language can be ambiguous. What does "negative 3 squared" mean or "the negative of 3 squared"?

$- {3}^{2} = - \left({3}^{2}\right) = - \left(9\right) = - 9$

${\left(- 3\right)}^{2} = \left(- 3\right) \cdot \left(- 3\right) = 9$