Find the value of the following (27)^-1/3

1.	Find the value of the following (27)^-1/3
Answer» ANSWER: $\large\boxed{\sf{\dfrac{1}{3}}}$ Step-by-step explanation: To FIND the value of, ${(27)}^{ - \frac{1}{3} }$ We know that, $27 = {3}^{3}$ THEREFORE, substituting the VALUES, we get, $= {( {3}^{3}) }^{ - \frac{1}{3} }$ Now, we know that, ${( {a}^{m} )}^{n} = {a}^{mn}$ Therefore, we will get, $= {3}^{3 \times ( - \frac{1}{3}) } \\ \\ = {3}^{ - 3 \times \frac{1}{3} }$ Therefore, we will get, $= {3}^{ - 1}$ But, we know that, ${x}^{ - 1} = \dfrac{1}{x}$ Therefore, we will get, $= \dfrac{1}{3}$ HENCE, the required value is 1/3.

Answer»

$\large\boxed{\sf{\dfrac{1}{3}}}$