Divide (12x^6+54x)/6

$\frac{12 x^{6} + 54 x}{6}$

Step 1

Factor $6 x$ out of $12 x^{6} + 54 x$ .

Factor $6 x$ out of $12 x^{6}$ .

$\frac{6 x (2 x^{5}) + 54 x}{6}$

Factor $6 x$ out of $54 x$ .

$\frac{6 x (2 x^{5}) + 6 x (9)}{6}$

Factor $6 x$ out of $6 x (2 x^{5}) + 6 x (9)$ .

$\frac{6 x (2 x^{5} + 9)}{6}$

Step 2

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x (2 x^{5} + 9)}{6}$

Divide $x (2 x^{5} + 9)$ by $1$ .

$x (2 x^{5} + 9)$

Step 3

Apply the distributive property.

$x (2 x^{5}) + x \cdot 9$

Step 4

Rewrite using the commutative property of multiplication.

$2 x \cdot x^{5} + x \cdot 9$

Step 5

Move $9$ to the left of $x$ .

$2 x \cdot x^{5} + 9 \cdot x$

Step 6

Multiply $x$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$2 (x^{5} x) + 9 \cdot x$

Multiply $x^{5}$ by $x$ .

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

$2 (x^{5} x^{1}) + 9 \cdot x$

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

$2 x^{5 + 1} + 9 \cdot x$

Add $5$ and $1$ .

$2 x^{6} + 9 \cdot x$

$2 x^{6} + 9 x$