Chapter 7.1, Problem 11CYU

To determine

To simplify:An expression ${\left[{\left(3^2\right)}^2\right]}^2$ .

Answer to Problem 11CYU

The required answer is $3^8$ .

Explanation of Solution

Given information:

The given expression is ${\left[{\left(3^2\right)}^2\right]}^2$ .

Calculation:

The given expression:

$={\left[{\left(3^2\right)}^2\right]}^2$

$={\left(3^{2\cdot 2}\right)}^2$

(Power of a power)

$={\left(3^4\right)}^2$

(Simplify)

$=3^{4\cdot 2}$

(Power of a power)

$=3^8$

(Simplify)

So, the required answer is $3^8$ .