Simplify 3^(x+2)9^(x-1)3^2

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Algebra

Simplify 3^(x+2)*9^(x-1)*3^2

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

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

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Move $3^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

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

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

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

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

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

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

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

Add $x$ and $2 x$ .

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

Subtract $2$ from $4$ .

$3^{3 x + 2}$

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