Simplify 3^( square root of 5+1)*3^(3- square root of 5)

$3^{\sqrt{5} + 1} \cdot 3^{3 - \sqrt{5}}$

Multiply $3^{\sqrt{5} + 1}$ by $3^{3 - \sqrt{5}}$ by adding the exponents.

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

$3^{\sqrt{5} + 1 + 3 - \sqrt{5}}$

Subtract $\sqrt{5}$ from $\sqrt{5}$ .

$3^{0 + 1 + 3}$

Add $0$ and $1$ .

$3^{1 + 3}$

Add $1$ and $3$ .

$3^{4}$

Raise $3$ to the power of $4$ .

$81$