Find the Third Term a_n=4(4)^n

$a_{n} = 4 {(4)}^{n}$

Substitute in the value of $n$ to find the $n$ th term.

$a_{3} = 4 {(4)}^{3}$

Multiply $4$ by ${(4)}^{3}$ by adding the exponents.

Multiply $4$ by ${(4)}^{3}$ .

Raise $4$ to the power of $1$ .

$a_{3} = 4 {(4)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a_{3} = 4^{1 + 3}$

Add $1$ and $3$ .

$a_{3} = 4^{4}$

Raise $4$ to the power of $4$ .

$a_{3} = 256$