Question

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

Answer 1

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.