Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

$3^{0 + 1 + 3}$

Step 1.3

Add $0$ and $1$ .

$3^{1 + 3}$

Step 1.4

Add $1$ and $3$ .

$3^{4}$

Step 2

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

$81$