Algebra Examples

$3^{x + 2} \cdot 9^{x - 1} \cdot 3^{2}$

Step 1

Multiply $3^{x + 2}$ by $3^{2}$ by adding the exponents.

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Step 1.1

Move $3^{2}$ .

$3^{2} \cdot 3^{x + 2} \cdot 9^{x - 1}$

Step 1.2

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

$3^{2 + x + 2} \cdot 9^{x - 1}$

Step 1.3

Add $2$ and $2$ .

$3^{x + 4} \cdot 9^{x - 1}$

Step 2

Multiply $3^{x + 4} \cdot 9^{x - 1}$ .

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$3^{x + 4} \cdot {(3^{2})}^{x - 1}$

Step 2.2

Multiply the exponents in ${(3^{2})}^{x - 1}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{x + 4} \cdot 3^{2 (x - 1)}$

Step 2.2.2

Apply the distributive property.

$3^{x + 4} \cdot 3^{2 x + 2 \cdot - 1}$

Step 2.2.3

Multiply $2$ by $- 1$ .

$3^{x + 4} \cdot 3^{2 x - 2}$

Step 2.3

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

$3^{x + 4 + 2 x - 2}$

Step 2.4

Add $x$ and $2 x$ .

$3^{3 x + 4 - 2}$

Step 2.5

Subtract $2$ from $4$ .

$3^{3 x + 2}$