Solve for a4 a_4=(2^4)/(3(4)^2)

$a_{4} = \frac{2^{4}}{3 {(4)}^{2}}$

Step 1

Simplify the expression.

Raise $2$ to the power of $4$ .

$a_{4} = \frac{16}{3 \cdot 4^{2}}$

Raise $4$ to the power of $2$ .

$a_{4} = \frac{16}{3 \cdot 16}$

Multiply $3$ by $16$ .

$a_{4} = \frac{16}{48}$

$a_{4} = \frac{16}{48}$

Step 2

Cancel the common factor of $16$ and $48$ .

Factor $16$ out of $16$ .

$a_{4} = \frac{16 (1)}{48}$

Cancel the common factors.

Factor $16$ out of $48$ .

$a_{4} = \frac{16 \cdot 1}{16 \cdot 3}$

Cancel the common factor.

$a_{4} = \frac{16 \cdot 1}{16 \cdot 3}$

Rewrite the expression.

$a_{4} = \frac{1}{3}$

$a_{4} = \frac{1}{3}$

$a_{4} = \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a_{4} = \frac{1}{3}$

Decimal Form:

$a_{4} = 0.\overline{3}$

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