Question

Find the value of $({216^{\dfrac{{ - 2}}{3}}})$ .
A.$\dfrac{1}{{36}}$
B.$\dfrac{1}{{256}}$
C.$\dfrac{1}{{16}}$
D.None of these

Answer 1

Hint: First we will find the cubic of $216$ . The dividend value changes into divisor value. It means the value to change from negative sign to positive sign we have to reciprocal to 6. Using these rules, we will find the correct solution for this question.

Complete step-by-step answer:
Given question is,
${216^{\dfrac{{ - 2}}{3}}}$
Here power value has negative value so it will be changing to Divisor of $1$ .
.$ = \dfrac{1}{{{{216}^{\dfrac{2}{3}}}}}$ (Now Changing into positive value. This means we will take reciprocal for this value)
Then we will find the cubic root of question value.
$ = \dfrac{1}{{{{({6^3})}^{\dfrac{2}{3}}}}}$ (Here $6$ is the cubic root of $216$)
Here cubic $3$ will be cancelled for power value $3$.
$\therefore $ the final value is $\dfrac{1}{{{6^2}}}$
So, the answer is $\dfrac{1}{{36}}$
Here option A is the correct answer for this question.

Additional information:
The number that is divided is called the dividend and the number which the dividend is being divided by is the divisor. The answer to a division problem is the quotient. The reciprocal is simply $\dfrac{1}{{number}}$. To get the reciprocal of a number, we divide $1$ by the number.

Note: To find the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). So, simply speaking, the reciprocal of $\dfrac{a}{b}$ is $\dfrac{b}{a}$ . To find the reciprocal of a number, divide $1$ by the number. Here we will concentrate on the main what is the cubic and square root for the given question and the given equation.