Finite Math Examples

$2 \cdot 3^{\frac{k}{2}} \cdot 3^{2 - \frac{2 k}{4}}$

Step 1

Multiply $3^{\frac{k}{2}}$ by $3^{2 - \frac{2 k}{4}}$ by adding the exponents.

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Step 1.1

Move $3^{2 - \frac{2 k}{4}}$ .

$2 \cdot (3^{2 - \frac{2 k}{4}} \cdot 3^{\frac{k}{2}})$

Step 1.2

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

$2 \cdot 3^{2 - \frac{2 k}{4} + \frac{k}{2}}$

Step 1.3

Cancel the common factor of $2$ and $4$ .

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Step 1.3.1

Factor $2$ out of $2 k$ .

$2 \cdot 3^{2 - \frac{2 (k)}{4} + \frac{k}{2}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $4$ .

$2 \cdot 3^{2 - \frac{2 k}{2 \cdot 2} + \frac{k}{2}}$

Step 1.3.2.2

Cancel the common factor.

$2 \cdot 3^{2 - \frac{2 k}{2 \cdot 2} + \frac{k}{2}}$

Step 1.3.2.3

Rewrite the expression.

$2 \cdot 3^{2 - \frac{k}{2} + \frac{k}{2}}$

Step 1.4

Combine the opposite terms in $2 - \frac{k}{2} + \frac{k}{2}$ .

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Step 1.4.1

Add $- \frac{k}{2}$ and $\frac{k}{2}$ .

$2 \cdot 3^{2 + 0}$

Step 1.4.2

Add $2$ and $0$ .

$2 \cdot 3^{2}$

Step 2

Raise $3$ to the power of $2$ .

$2 \cdot 9$

Step 3

Multiply $2$ by $9$ .

$18$