Simplify ((10x^4)^2)/((5x^2)^3)

$\frac{{(10 x^{4})}^{2}}{{(5 x^{2})}^{3}}$

Simplify the numerator.

Apply the product rule to $10 x^{4}$ .

$\frac{10^{2} {(x^{4})}^{2}}{{(5 x^{2})}^{3}}$

Raise $10$ to the power of $2$ .

$\frac{100 {(x^{4})}^{2}}{{(5 x^{2})}^{3}}$

Multiply the exponents in ${(x^{4})}^{2}$ .

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

$\frac{100 x^{4 \cdot 2}}{{(5 x^{2})}^{3}}$

Multiply $4$ by $2$ .

$\frac{100 x^{8}}{{(5 x^{2})}^{3}}$

Simplify the denominator.

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

$\frac{100 x^{8}}{5^{3} {(x^{2})}^{3}}$

Raise $5$ to the power of $3$ .

$\frac{100 x^{8}}{125 {(x^{2})}^{3}}$

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

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

$\frac{100 x^{8}}{125 x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{100 x^{8}}{125 x^{6}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $100$ and $125$ .

Factor $25$ out of $100 x^{8}$ .

$\frac{25 (4 x^{8})}{125 x^{6}}$

Cancel the common factors.

Factor $25$ out of $125 x^{6}$ .

$\frac{25 (4 x^{8})}{25 (5 x^{6})}$

Cancel the common factor.

$\frac{25 (4 x^{8})}{25 (5 x^{6})}$

Rewrite the expression.

$\frac{4 x^{8}}{5 x^{6}}$

Cancel the common factor of $x^{8}$ and $x^{6}$ .

Factor $x^{6}$ out of $4 x^{8}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{4 x^{2}}{5}$