Write the Fraction in Simplest Form ((5v^3)^3)/(2v^10)

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

Simplify the numerator.

Apply the product rule to $5 v^{3}$ .

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

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

$\frac{125 {(v^{3})}^{3}}{2 v^{10}}$

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

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

$\frac{125 v^{3 \cdot 3}}{2 v^{10}}$

Multiply $3$ by $3$ .

$\frac{125 v^{9}}{2 v^{10}}$

Cancel the common factor of $v^{9}$ and $v^{10}$ .

Factor $v^{9}$ out of $125 v^{9}$ .

$\frac{v^{9} \cdot 125}{2 v^{10}}$

Cancel the common factors.

Factor $v^{9}$ out of $2 v^{10}$ .

$\frac{v^{9} \cdot 125}{v^{9} (2 v)}$

Cancel the common factor.

$\frac{v^{9} \cdot 125}{v^{9} (2 v)}$

Rewrite the expression.

$\frac{125}{2 v}$