Question

The number ${\left(6^{\left(6^6\right)}\right)}^{1/6}$ is equal to

• A. $6^6$
• B. $6^{6^6-1}$
• C. $\left(6^{\left(6^5\right)}\right)$
• D. $\left(6^{\left(5^6\right)}\right)$

Answer 1

The correct option is C $\left(6^{\left(6^5\right)}\right)$

The given expression ${\left(6^{\left(6^6\right)}\right)}^{\frac{1}{6}}$ can be simplified as follows:

${\left(6^{\left(6^6\right)}\right)}^{\frac{1}{6}}=\left(6^{(6^6\times \frac{1}{6})}\right)$ .......$(\because {\left(x^m\right)}^n=x^{m\times n})$

$=6^{\left(6^5\right)}$

Hence, ${\left(6^{\left(6^6\right)}\right)}^{\frac{1}{6}}=6^{\left(6^5\right)}$