Algebra Examples

$3^{5 x} \cdot 81^{1 - x}$

Step 1

Rewrite $81$ as $3^{4}$ .

$3^{5 x} \cdot {(3^{4})}^{1 - x}$

Step 2

Multiply the exponents in ${(3^{4})}^{1 - x}$ .

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Step 2.1

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

$3^{5 x} \cdot 3^{4 (1 - x)}$

Step 2.2

Apply the distributive property.

$3^{5 x} \cdot 3^{4 \cdot 1 + 4 (- x)}$

Step 2.3

Multiply $4$ by $1$ .

$3^{5 x} \cdot 3^{4 + 4 (- x)}$

Step 2.4

Multiply $- 1$ by $4$ .

$3^{5 x} \cdot 3^{4 - 4 x}$

Step 3

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

$3^{5 x + 4 - 4 x}$

Step 4

Subtract $4 x$ from $5 x$ .

$3^{x + 4}$