Question

(-27)^-1/3

Answer 1

this means the reciprocal of the cubed root of -27

Answer 2

the cube root of -27 is -

the reciprocal of -3 is
\[-\frac{1}{3}\]

Answer 3

exponent is also
\[-\frac{1}{3}\] but that is a coincidence

Answer 4

yea the exponent is 1/3

Answer 5

Could you please show me how this is worked? There is a lot of flipping I suppose or is it an automatic thing that is known? Since 3^3 is 27 if it's a -1/3 it's the reciprocal of the number cube which is also -1/3?

Answer 6

There is a lot going on in this problem. A negative 27, and a fractional exponent that is negative. The way I would do it, is remember a fractional exponent means
\[x^{-a}= \frac{1}{x^{a}}\]
the answer is 1 over something. so we know
\[(-27)^{-\frac{1}{3}}= \frac{1}{(-27)^{\frac{1}{3}}}\]
The 1/3 means take the cube root of -27. The only easy way to do this is memorize the cube root of numbers. In this case, 3 is the cube root of 27, and -3 is the cube root of -27
So we now have
\[\frac{1}{(-27)^{\frac{1}{3}}}=\frac{1}{-3}=-\frac{1}{3}\]
Practicing these problems helps...