Algebra Examples

$\frac{x^{6}}{x^{5}} \cdot 3 x^{2}$

Step 1

Rewrite using the commutative property of multiplication.

$3 \frac{x^{6}}{x^{5}} x^{2}$

Step 2

Cancel the common factor of $x^{6}$ and $x^{5}$ .

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Step 2.1

Factor $x^{5}$ out of $x^{6}$ .

$3 \frac{x^{5} x}{x^{5}} x^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$3 \frac{x^{5} x}{x^{5} \cdot 1} x^{2}$

Step 2.2.2

Cancel the common factor.

$3 \frac{x^{5} x}{x^{5} \cdot 1} x^{2}$

Step 2.2.3

Rewrite the expression.

$3 \frac{x}{1} x^{2}$

Step 2.2.4

Divide $x$ by $1$ .

$3 x \cdot x^{2}$

Step 3

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

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Step 3.1

Move $x^{2}$ .

$3 (x^{2} x)$

Step 3.2

Multiply $x^{2}$ by $x$ .

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Step 3.2.1

Raise $x$ to the power of $1$ .

$3 (x^{2} x^{1})$

Step 3.2.2

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

$3 x^{2 + 1}$

Step 3.3

Add $2$ and $1$ .

$3 x^{3}$