Simplify (5x^4(x^2))/((5x^6)^2)

$\frac{5 x^{4} (x^{2})}{{(5 x^{6})}^{2}}$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{5 (x^{2} x^{4})}{{(5 x^{6})}^{2}}$

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

$\frac{5 x^{2 + 4}}{{(5 x^{6})}^{2}}$

Add $2$ and $4$ .

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

Simplify the denominator.

Apply the product rule to $5 x^{6}$ .

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

Raise $5$ to the power of $2$ .

$\frac{5 x^{6}}{25 {(x^{6})}^{2}}$

Multiply the exponents in ${(x^{6})}^{2}$ .

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

$\frac{5 x^{6}}{25 x^{6 \cdot 2}}$

Multiply $6$ by $2$ .

$\frac{5 x^{6}}{25 x^{12}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $5$ and $25$ .

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

$\frac{5 (x^{6})}{25 x^{12}}$

Cancel the common factors.

Factor $5$ out of $25 x^{12}$ .

$\frac{5 (x^{6})}{5 (5 x^{12})}$

Cancel the common factor.

$\frac{5 x^{6}}{5 (5 x^{12})}$

Rewrite the expression.

$\frac{x^{6}}{5 x^{12}}$

Cancel the common factor of $x^{6}$ and $x^{12}$ .

Multiply by $1$ .

$\frac{x^{6} \cdot 1}{5 x^{12}}$

Cancel the common factors.

Factor $x^{6}$ out of $5 x^{12}$ .

$\frac{x^{6} \cdot 1}{x^{6} (5 x^{6})}$

Cancel the common factor.

$\frac{x^{6} \cdot 1}{x^{6} (5 x^{6})}$

Rewrite the expression.

$\frac{1}{5 x^{6}}$