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

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

Step 1

Simplify the denominator.

Apply the product rule to $2 m^{4} x^{5}$ .

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

Apply the product rule to $2 m^{4}$ .

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

Raise $2$ to the power of $4$ .

$\frac{6 x^{2}}{16 {(m^{4})}^{4} {(x^{5})}^{4}}$

Multiply the exponents in ${(m^{4})}^{4}$ .

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

$\frac{6 x^{2}}{16 m^{4 \cdot 4} {(x^{5})}^{4}}$

Multiply $4$ by $4$ .

$\frac{6 x^{2}}{16 m^{16} {(x^{5})}^{4}}$

Multiply the exponents in ${(x^{5})}^{4}$ .

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

$\frac{6 x^{2}}{16 m^{16} x^{5 \cdot 4}}$

Multiply $5$ by $4$ .

$\frac{6 x^{2}}{16 m^{16} x^{20}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6$ and $16$ .

Factor $2$ out of $6 x^{2}$ .

$\frac{2 (3 x^{2})}{16 m^{16} x^{20}}$

Cancel the common factors.

Factor $2$ out of $16 m^{16} x^{20}$ .

$\frac{2 (3 x^{2})}{2 (8 m^{16} x^{20})}$

Cancel the common factor.

$\frac{2 (3 x^{2})}{2 (8 m^{16} x^{20})}$

Rewrite the expression.

$\frac{3 x^{2}}{8 m^{16} x^{20}}$

Cancel the common factor of $x^{2}$ and $x^{20}$ .

Factor $x^{2}$ out of $3 x^{2}$ .

$\frac{x^{2} \cdot 3}{8 m^{16} x^{20}}$

Cancel the common factors.

Factor $x^{2}$ out of $8 m^{16} x^{20}$ .

$\frac{x^{2} \cdot 3}{x^{2} (8 m^{16} x^{18})}$

Cancel the common factor.

$\frac{x^{2} \cdot 3}{x^{2} (8 m^{16} x^{18})}$

Rewrite the expression.

$\frac{3}{8 m^{16} x^{18}}$