Simplify ((6y^3)^4)/(2y^5)

$\frac{{(6 y^{3})}^{4}}{2 y^{5}}$

Step 1

Simplify the numerator.

Apply the product rule to $6 y^{3}$ .

$\frac{6^{4} {(y^{3})}^{4}}{2 y^{5}}$

Raise $6$ to the power of $4$ .

$\frac{1296 {(y^{3})}^{4}}{2 y^{5}}$

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

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

$\frac{1296 y^{3 \cdot 4}}{2 y^{5}}$

Multiply $3$ by $4$ .

$\frac{1296 y^{12}}{2 y^{5}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $1296$ and $2$ .

Factor $2$ out of $1296 y^{12}$ .

$\frac{2 (648 y^{12})}{2 y^{5}}$

Cancel the common factors.

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

$\frac{2 (648 y^{12})}{2 (y^{5})}$

Cancel the common factor.

$\frac{2 (648 y^{12})}{2 y^{5}}$

Rewrite the expression.

$\frac{648 y^{12}}{y^{5}}$

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

Factor $y^{5}$ out of $648 y^{12}$ .

$\frac{y^{5} (648 y^{7})}{y^{5}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{5} (648 y^{7})}{y^{5} \cdot 1}$

Cancel the common factor.

$\frac{y^{5} (648 y^{7})}{y^{5} \cdot 1}$

Rewrite the expression.

$\frac{648 y^{7}}{1}$

Divide $648 y^{7}$ by $1$ .

$648 y^{7}$