Algebra Examples

$3^{a} \cdot 3^{b} \div 3^{c} \div 3^{d}$

Step 1

Rewrite the division as a fraction.

$\frac{3^{a} \cdot 3^{b} \div 3^{c}}{3^{d}}$

Step 2

Cancel the common factor of $3^{a}$ and $3^{c}$ .

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Step 2.1

Factor $3^{c}$ out of $3^{a} \cdot 3^{b}$ .

$\frac{3^{c} (3^{a - c} \cdot 3^{b}) \div 3^{c}}{3^{d}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{3^{c} (3^{a - c} \cdot 3^{b}) \div 3^{c} \cdot 1}{3^{d}}$

Step 2.2.2

Cancel the common factor.

$\frac{3^{c} (3^{a - c} \cdot 3^{b}) \div 3^{c} \cdot 1}{3^{d}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{3^{a - c} \cdot 3^{b}}{1}}{3^{d}}$

Step 2.2.4

Divide $3^{a - c} \cdot 3^{b}$ by $1$ .

$\frac{3^{a - c} \cdot 3^{b}}{3^{d}}$

Step 3

Cancel the common factor of $3^{a - c}$ and $3^{d}$ .

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Step 3.1

Factor $3^{d}$ out of $3^{a - c} \cdot 3^{b}$ .

$\frac{3^{d} (3^{a - c - d} \cdot 3^{b})}{3^{d}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{3^{d} (3^{a - c - d} \cdot 3^{b})}{3^{d} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{3^{d} (3^{a - c - d} \cdot 3^{b})}{3^{d} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{3^{a - c - d} \cdot 3^{b}}{1}$

Step 3.2.4

Divide $3^{a - c - d} \cdot 3^{b}$ by $1$ .

$3^{a - c - d} \cdot 3^{b}$

Step 4

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

$3^{a - c - d + b}$