Question

im confused about how to evaluate this expression

please look at drawing

Answer 1

\(\huge a^{\frac{n}{m}} = \sqrt[m]{a^n}\)

Answer 2

in order to solve it I put it like this \[\sqrt[2]{-16}^{3}\]

Answer 3

yeap

Answer 4

but it doesn't make sense cause if I use -4 times itself I would get a positive 16 when I have a negative number to get

Answer 5

have you done imaginary numbers yet?

Answer 6

hmm no.

Answer 7

hmmm

Answer 8

ok... then I gather ... \(\huge -16^{\frac{3}{2}}\implies-\sqrt[2]{16^3}\)

Answer 9

the -negative will go inside the root only if grouped together with the coefficient

Answer 10

(-4)(-4)

Answer 11

I see

Answer 12

so keep in mind that \(\huge -16^{\frac{3}{2}}\ne (-16)^{\frac{3}{2}}\)

Answer 13

oh okay so my end result will be a positive 64 correct?

Answer 14

so let us simplify 16

\(\bf -16^{\frac{3}{2}}\implies-\sqrt[2]{16^3}\\ \quad \\
16 \implies 2\times 2\times 2\times 2\implies 2^4\\ \quad \\
-\sqrt[2]{16^3}\implies -\sqrt{(2^4)^3}\implies -\sqrt{2^{12}}\implies -\sqrt{(2^6)^2}\)

well, don't forget the " - " in front of it