Rational exponents evaluate each expression. (a) 27^(1/3) (b) (-8)^(1/3) (c) -(1/8)^(1/3)

(a) Definition used:
Definition of rational exponents:
"For any rational exponent m/n in its lowest terms, where m and n are integers and ${\displaystyle n>0\text{we define,}{\displaystyle {\left(a\right)}^{\frac{m}{n}}=\sqrt[n]{{\left(a\right)}^m}={\left(\sqrt[n]{a}\right)}^m.}}$
Formula used:
Laws of exponents:
"To raise a power to a new power, multiply the exponents".
${\displaystyle {\left(a^m\right)}^n=a^{mn}}$
Calculation:
The given expression is ${\displaystyle {27}^{\frac{1}{3}}.}$
Use the above mentioned definition and simplify the expression as shown below.
${\displaystyle {27}^{\frac{1}{3}}={(3\times 3\times 3)}^{\frac{1}{3}}}$
${\displaystyle ={\left(3^3\right)}^{\frac{1}{3}}}$
${\displaystyle =3^{3\times \frac{1}{3}}}$
$=3$
Thus, the value of the expression ${\displaystyle {27}^{\frac{1}{3}}}$ is 3.
(b) Use the above definition and formula mentioned in sub part (a) and simplify the expression as shown below.
${\displaystyle {(-8)}^{\frac{1}{3}}={((-2)\times (-2)\times (-2))}^{\frac{1}{3}}}$
${\displaystyle ={(-2)}^{3\times \frac{1}{3}}}$
${\displaystyle ={(-2)}^{3\times \frac{1}{3}}}$
$=-2$
Thus, the value of the expression ${\displaystyle {(-8)}^{\frac{1}{3}}}$ is (-2).
(c) Use the above definition and formula mentioned in sub part (a) and simplify the expression as shown below.
${\displaystyle -{\left(\frac{1}{8}\right)}^{\frac{1}{3}}=-{\left(\frac{1}{2^3}\right)}^{\frac{1}{3}}}$
${\displaystyle =-{\left(2^{-3}\right)}^{\frac{1}{3}}}$
${\displaystyle =-\left(2^{-3\times \frac{1}{3}}\right)}$
On further simplifications, the following is obtained.
${\displaystyle -{\left(\frac{1}{8}\right)}^{\frac{1}{3}}=-\left(2^{-1}\right)}$
${\displaystyle =(-\frac{1}{2})}$
Thus, the value of the expression ${\displaystyle -{\left(\frac{1}{8}\right)}^{\frac{1}{3}}\text{is}{\displaystyle =(-\frac{1}{2}).}}$