Simplify (9x^38)/(6(x^6)^3x)

$\frac{9 x^{38}}{6 {(x^{6})}^{3} x}$

Step 1

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9 x^{38}$ .

$\frac{3 (3 x^{38})}{6 {(x^{6})}^{3} x}$

Cancel the common factors.

Factor $3$ out of $6 {(x^{6})}^{3} x$ .

$\frac{3 (3 x^{38})}{3 (2 {(x^{6})}^{3} x)}$

Cancel the common factor.

$\frac{3 (3 x^{38})}{3 (2 {(x^{6})}^{3} x)}$

Rewrite the expression.

$\frac{3 x^{38}}{2 {(x^{6})}^{3} x}$

Step 2

Cancel the common factor of $x^{38}$ and $x$ .

Factor $x$ out of $3 x^{38}$ .

$\frac{x (3 x^{37})}{2 {(x^{6})}^{3} x}$

Cancel the common factors.

Factor $x$ out of $2 {(x^{6})}^{3} x$ .

$\frac{x (3 x^{37})}{x (2 {(x^{6})}^{3})}$

Cancel the common factor.

$\frac{x (3 x^{37})}{x (2 {(x^{6})}^{3})}$

Rewrite the expression.

$\frac{3 x^{37}}{2 {(x^{6})}^{3}}$

Step 3

Multiply the exponents in ${(x^{6})}^{3}$ .

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

$\frac{3 x^{37}}{2 x^{6 \cdot 3}}$

Multiply $6$ by $3$ .

$\frac{3 x^{37}}{2 x^{18}}$

Step 4

Cancel the common factor of $x^{37}$ and $x^{18}$ .

Factor $x^{18}$ out of $3 x^{37}$ .

$\frac{x^{18} (3 x^{19})}{2 x^{18}}$

Cancel the common factors.

Factor $x^{18}$ out of $2 x^{18}$ .

$\frac{x^{18} (3 x^{19})}{x^{18} \cdot 2}$

Cancel the common factor.

$\frac{x^{18} (3 x^{19})}{x^{18} \cdot 2}$

Rewrite the expression.

$\frac{3 x^{19}}{2}$