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

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

Step 1

Cancel the common factor of $5$ and $10$ .

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

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

Cancel the common factors.

Factor $5$ out of $10 x^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Multiply the exponents in ${(x^{5})}^{3}$ .

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

$\frac{x^{5 \cdot 3}}{2 x^{5}}$

Multiply $5$ by $3$ .

$\frac{x^{15}}{2 x^{5}}$

Step 3

Cancel the common factor of $x^{15}$ and $x^{5}$ .

Factor $x^{5}$ out of $x^{15}$ .

$\frac{x^{5} x^{10}}{2 x^{5}}$

Cancel the common factors.

Factor $x^{5}$ out of $2 x^{5}$ .

$\frac{x^{5} x^{10}}{x^{5} \cdot 2}$

Cancel the common factor.

$\frac{x^{5} x^{10}}{x^{5} \cdot 2}$

Rewrite the expression.

$\frac{x^{10}}{2}$