Question

Express ${\left[{\left\{{\left(3\right)}^2\right\}}^3\right]}^0$ using a single exponent.

Answer 1

In ${\left[{\left\{{\left(3\right)}^2\right\}}^3\right]}^0$,

First we will start from the innermost bracket,

${\left(3\right)}^2=3\times 3=9$.

${\left[{\left\{{\left(3\right)}^2\right\}}^3\right]}^0$$={\left[{\left\{9\right\}}^3\right]}^0$

Now, $9^3=9\times 9\times 9=729$

So, ${\left[{\left\{9\right\}}^3\right]}^0={\left(729\right)}^0$.

We know, $a^0=1$

So, ${\left(729\right)}^0=1$

Therefore, ${\left[{\left\{{\left(3\right)}^2\right\}}^3\right]}^0$$=1$.