Question

Simplify the expression

${\left[{\left(2^2\right)}^2\right]}^4$

Short answer

The simplified version of${\left[{\left(2^2\right)}^2\right]}^4$ is 65536.

Step-by-step solution

Step 1. State the ‘Law of indices’ for power of index numbers.

If a term with a power is itself raised to a power then the powers are multiplied together.

In general:${\left(x^m\right)}^n=x^{m\times n}$

Step 2. Simplify the expression.

Apply the brackets rule and simplify the given expression.

$$\begin{gathered} {\left[{\left(2^2\right)}^2\right]}^4={\left[2^{2\times 2}\right]}^4 \\ ={\left[2^4\right]}^4 \\ =2^{4\times 4} \\ =2^{16} \\ =65536 \end{gathered}$$

Step 3. State the conclusion.

Thus the simplification of${\left[{\left(2^2\right)}^2\right]}^4$ is 65536.