Write the Fraction in Simplest Form ((2v^4)^3)/(10v^5)

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

Simplify the numerator.

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

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

Raise $2$ to the power of $3$ .

$\frac{8 {(v^{4})}^{3}}{10 v^{5}}$

Multiply the exponents in ${(v^{4})}^{3}$ .

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

$\frac{8 v^{4 \cdot 3}}{10 v^{5}}$

Multiply $4$ by $3$ .

$\frac{8 v^{12}}{10 v^{5}}$

Cancel the common factor of $8$ and $10$ .

Factor $2$ out of $8 v^{12}$ .

$\frac{2 (4 v^{12})}{10 v^{5}}$

Cancel the common factors.

Factor $2$ out of $10 v^{5}$ .

$\frac{2 (4 v^{12})}{2 (5 v^{5})}$

Cancel the common factor.

$\frac{2 (4 v^{12})}{2 (5 v^{5})}$

Rewrite the expression.

$\frac{4 v^{12}}{5 v^{5}}$

Cancel the common factor of $v^{12}$ and $v^{5}$ .

Factor $v^{5}$ out of $4 v^{12}$ .

$\frac{v^{5} (4 v^{7})}{5 v^{5}}$

Cancel the common factors.

Factor $v^{5}$ out of $5 v^{5}$ .

$\frac{v^{5} (4 v^{7})}{v^{5} \cdot 5}$

Cancel the common factor.

$\frac{v^{5} (4 v^{7})}{v^{5} \cdot 5}$

Rewrite the expression.

$\frac{4 v^{7}}{5}$