Write the Fraction in Simplest Form ((3a^4)^5)/(4a)

$\frac{{(3 a^{4})}^{5}}{4 a}$

Simplify the numerator.

Apply the product rule to $3 a^{4}$ .

$\frac{3^{5} {(a^{4})}^{5}}{4 a}$

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

$\frac{243 {(a^{4})}^{5}}{4 a}$

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

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

$\frac{243 a^{4 \cdot 5}}{4 a}$

Multiply $4$ by $5$ .

$\frac{243 a^{20}}{4 a}$

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

Factor $a$ out of $243 a^{20}$ .

$\frac{a (243 a^{19})}{4 a}$

Cancel the common factors.

Factor $a$ out of $4 a$ .

$\frac{a (243 a^{19})}{a \cdot 4}$

Cancel the common factor.

$\frac{a (243 a^{19})}{a \cdot 4}$

Rewrite the expression.

$\frac{243 a^{19}}{4}$