MCQ
The value of $4^{2^{2^{1^{5^6}}}}$ is
- A$(256)^{30}$
- B$4^{120}$
- C$4^8$
- ✓$2^8$
✓
Answer
Correct option: D.
$2^8$
(d)
We know that $1^{5^6}=1$
$\therefore \quad 2^{1^{5^6}}=2^1=2 \Rightarrow 2^{2^{1^{5^6}}}=2^2=4 \Rightarrow 4^{2^{2^{1^{5^6}}}}=4^4=\left(2^2\right)^4=2^8$
We know that $1^{5^6}=1$
$\therefore \quad 2^{1^{5^6}}=2^1=2 \Rightarrow 2^{2^{1^{5^6}}}=2^2=4 \Rightarrow 4^{2^{2^{1^{5^6}}}}=4^4=\left(2^2\right)^4=2^8$
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