Question

Simplify to a single power of 2:

(2²)^4

Answer 1

`\bf\implies \: {2}^(8)`

Explanation:

We know that,

The exponent (^) rule to solve this problem that is :

`\: \: \: \: \: \: \: \: \: \: \: \: \bf \longrightarrow \: {(a^(m))}^(n) = {(a)}^(m * n)`

According to the question :-

`\bf \longrightarrow \: {(2^(2)) }^(4)`

`\bf \longrightarrow \: (2)^(2 * 4)`

`\bf\longrightarrow \: {2}^(8) \: \boxed { \bf \: \red{ ans.}}`

Answer 2

`\sf 2^(8)`

Explanation:

Exponent rule:

`\sf \boxed{(a^m)^n=a^(m*n)}`

To convert to single power, multiply the powers.

`\sf (2^2)^4= 2^(2*4)`

`\sf =2^8`