Question

Simplify the expression

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

Short answer

The simplified version of${\left[{\left(3^2\right)}^2\right]}^2$ is 6561.

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.

$$\begin{gathered} {\left[{\left(3^2\right)}^2\right]}^2={\left[3^{2\times 2}\right]}^2 \\ ={\left[3^4\right]}^2 \\ =3^{4\times 2} \\ =3^8 \\ =6561 \end{gathered}$$

Step 3. State the conclusion.

Thus the simplification of${\left[{\left(3^2\right)}^2\right]}^2$is 6561.