Question

plz bro give solution of this.spams will be reported.​

Answer 1

Answer:

d)

${6}^{3} \times 2$

Step-by-step explanation:

To find ---->

$value \: of \: \\ \sqrt{ {3}^{2} \sqrt{ {9}^{2} \sqrt{ {81}^{2 } \sqrt{ {16}^{16} } } } }$

Concept used---->

1)

$\sqrt{ {x}^{m} } \: = {x}^{ \frac{m}{2} }$

2)

${a}^{m} \: {a}^{n} \: = {a}^{m + n}$

3)

$( \: {a}^{m} \: ) ^{n} \: = {a}^{m \: n}$

Solution----> ATQ,

$\sqrt{ {3}^{2} \sqrt{ {9}^{2} \sqrt{ {81}^{2} \sqrt{ {16}^{16} } } } }$

$= \sqrt{ {3}^{2} \sqrt{ {9}^{2} \times \sqrt{ {81}^{2} \times {16}^{8} } } }$

$= \sqrt{ {3}^{2} \sqrt{ {9}^{2} \times {81} \times {16}^{4} } }$

$= \sqrt{ {3}^{2} \times 9 \times 9 \times {16}^{2} }$

$= 3 \times 3 \times 3 \times 16$

$= {3}^{3} \times {2}^{4}$

$= {3}^{3} \times {2}^{3 + 1}$

$= {3}^{3} \times {2}^{3} \times 2$

$= ( \: 3 \times 2 \: ) ^{3} \times 2$

$= ( \: 6 \: ) ^{3} \times 2$

$= {6}^{3} \times 2$