(-27)^-1/3

this means the reciprocal of the cubed root of -27

the cube root of -27 is - the reciprocal of -3 is \[-\frac{1}{3}\]

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

yea the exponent is 1/3

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?

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...

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