Simplify ((x^2)^35x)/(6x^215x^3)

$\frac{{(x^{2})}^{3} \cdot 5 x}{6 x^{2} \cdot 15 x^{3}}$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{{(x^{2})}^{3} \cdot (5 x)}{6 (x^{3} x^{2}) \cdot 15}$

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

$\frac{{(x^{2})}^{3} \cdot (5 x)}{6 x^{3 + 2} \cdot 15}$

Add $3$ and $2$ .

$\frac{{(x^{2})}^{3} \cdot (5 x)}{6 x^{5} \cdot 15}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of ${(x^{2})}^{3} \cdot (5 x)$ .

$\frac{5 ({(x^{2})}^{3} \cdot (x))}{6 x^{5} \cdot 15}$

Cancel the common factors.

Factor $5$ out of $6 x^{5} \cdot 15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

Factor $x$ out of $6 x^{5} \cdot 3$ .

$\frac{x \cdot {(x^{2})}^{3}}{x (6 x^{4} \cdot 3)}$

Cancel the common factor.

$\frac{x \cdot {(x^{2})}^{3}}{x (6 x^{4} \cdot 3)}$

Rewrite the expression.

$\frac{{(x^{2})}^{3}}{6 x^{4} \cdot 3}$

Simplify the expression.

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$\frac{x^{2 \cdot 3}}{6 x^{4} \cdot 3}$

Multiply $2$ by $3$ .

$\frac{x^{6}}{6 x^{4} \cdot 3}$

Multiply $3$ by $6$ .

$\frac{x^{6}}{18 x^{4}}$

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $x^{6}$ .

$\frac{x^{4} x^{2}}{18 x^{4}}$

Cancel the common factors.

Factor $x^{4}$ out of $18 x^{4}$ .

$\frac{x^{4} x^{2}}{x^{4} \cdot 18}$

Cancel the common factor.

$\frac{x^{4} x^{2}}{x^{4} \cdot 18}$

Rewrite the expression.

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

Simplify ((x^2)^3*5x)/(6x^2*15x^3)

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Simplify ((x^2)^35x)/(6x^215x^3)