Simplify (8w^3y^11)/((4w^3y^5)^2)

$\frac{8 w^{3} y^{11}}{{(4 w^{3} y^{5})}^{2}}$

Step 1

Simplify the denominator.

Apply the product rule to $4 w^{3} y^{5}$ .

$\frac{8 w^{3} y^{11}}{{(4 w^{3})}^{2} {(y^{5})}^{2}}$

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

$\frac{8 w^{3} y^{11}}{4^{2} {(w^{3})}^{2} {(y^{5})}^{2}}$

Raise $4$ to the power of $2$ .

$\frac{8 w^{3} y^{11}}{16 {(w^{3})}^{2} {(y^{5})}^{2}}$

Multiply the exponents in ${(w^{3})}^{2}$ .

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

$\frac{8 w^{3} y^{11}}{16 w^{3 \cdot 2} {(y^{5})}^{2}}$

Multiply $3$ by $2$ .

$\frac{8 w^{3} y^{11}}{16 w^{6} {(y^{5})}^{2}}$

Multiply the exponents in ${(y^{5})}^{2}$ .

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

$\frac{8 w^{3} y^{11}}{16 w^{6} y^{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\frac{8 w^{3} y^{11}}{16 w^{6} y^{10}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $16$ .

Factor $8$ out of $8 w^{3} y^{11}$ .

$\frac{8 (w^{3} y^{11})}{16 w^{6} y^{10}}$

Cancel the common factors.

Factor $8$ out of $16 w^{6} y^{10}$ .

$\frac{8 (w^{3} y^{11})}{8 (2 w^{6} y^{10})}$

Cancel the common factor.

$\frac{8 (w^{3} y^{11})}{8 (2 w^{6} y^{10})}$

Rewrite the expression.

$\frac{w^{3} y^{11}}{2 w^{6} y^{10}}$

Cancel the common factor of $w^{3}$ and $w^{6}$ .

Factor $w^{3}$ out of $w^{3} y^{11}$ .

$\frac{w^{3} (y^{11})}{2 w^{6} y^{10}}$

Cancel the common factors.

Factor $w^{3}$ out of $2 w^{6} y^{10}$ .

$\frac{w^{3} (y^{11})}{w^{3} (2 w^{3} y^{10})}$

Cancel the common factor.

$\frac{w^{3} y^{11}}{w^{3} (2 w^{3} y^{10})}$

Rewrite the expression.

$\frac{y^{11}}{2 w^{3} y^{10}}$

Cancel the common factor of $y^{11}$ and $y^{10}$ .

Factor $y^{10}$ out of $y^{11}$ .

$\frac{y^{10} y}{2 w^{3} y^{10}}$

Cancel the common factors.

Factor $y^{10}$ out of $2 w^{3} y^{10}$ .

$\frac{y^{10} y}{y^{10} (2 w^{3})}$

Cancel the common factor.

$\frac{y^{10} y}{y^{10} (2 w^{3})}$

Rewrite the expression.

$\frac{y}{2 w^{3}}$

Simplify (8w^3y^11)/((4w^3y^5)^2)

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