Write the Fraction in Simplest Form ((3y^5)^3)/(2y^6)

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

Step 1

Simplify the numerator.

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

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

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

$\frac{27 {(y^{5})}^{3}}{2 y^{6}}$

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

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

$\frac{27 y^{5 \cdot 3}}{2 y^{6}}$

Multiply $5$ by $3$ .

$\frac{27 y^{15}}{2 y^{6}}$

Step 2

Cancel the common factor of $y^{15}$ and $y^{6}$ .

Factor $y^{6}$ out of $27 y^{15}$ .

$\frac{y^{6} (27 y^{9})}{2 y^{6}}$

Cancel the common factors.

Factor $y^{6}$ out of $2 y^{6}$ .

$\frac{y^{6} (27 y^{9})}{y^{6} \cdot 2}$

Cancel the common factor.

$\frac{y^{6} (27 y^{9})}{y^{6} \cdot 2}$

Rewrite the expression.

$\frac{27 y^{9}}{2}$