Simplify (((2xy)/(w^2))^3)÷((24x^2)/(w^5))

${(\frac{2 x y}{w^{2}})}^{3} \div \frac{24 x^{2}}{w^{5}}$

To divide by a fraction, multiply by its reciprocal.

${(\frac{2 x y}{w^{2}})}^{3} \frac{w^{5}}{24 x^{2}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 x y}{w^{2}}$ .

$\frac{{(2 x y)}^{3}}{{(w^{2})}^{3}} \cdot \frac{w^{5}}{24 x^{2}}$

Apply the product rule to $2 x y$ .

$\frac{{(2 x)}^{3} y^{3}}{{(w^{2})}^{3}} \cdot \frac{w^{5}}{24 x^{2}}$

Apply the product rule to $2 x$ .

$\frac{2^{3} x^{3} y^{3}}{{(w^{2})}^{3}} \cdot \frac{w^{5}}{24 x^{2}}$

Combine.

$\frac{2^{3} x^{3} y^{3} w^{5}}{{(w^{2})}^{3} (24 x^{2})}$

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $2^{3} x^{3} y^{3} w^{5}$ .

$\frac{x^{2} (2^{3} x y^{3} w^{5})}{{(w^{2})}^{3} (24 x^{2})}$

Cancel the common factors.

Factor $x^{2}$ out of ${(w^{2})}^{3} (24 x^{2})$ .

$\frac{x^{2} (2^{3} x y^{3} w^{5})}{x^{2} ({(w^{2})}^{3} \cdot (24))}$

Cancel the common factor.

$\frac{x^{2} (2^{3} x y^{3} w^{5})}{x^{2} ({(w^{2})}^{3} \cdot (24))}$

Rewrite the expression.

$\frac{2^{3} x y^{3} w^{5}}{{(w^{2})}^{3} \cdot (24)}$

Simplify the expression.

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

$\frac{8 x y^{3} w^{5}}{{(w^{2})}^{3} \cdot 24}$

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

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

$\frac{8 x y^{3} w^{5}}{w^{2 \cdot 3} \cdot 24}$

Multiply $2$ by $3$ .

$\frac{8 x y^{3} w^{5}}{w^{6} \cdot 24}$

Cancel the common factor of $8$ and $24$ .

Factor $8$ out of $8 x y^{3} w^{5}$ .

$\frac{8 (x y^{3} w^{5})}{w^{6} \cdot 24}$

Cancel the common factors.

Factor $8$ out of $w^{6} \cdot 24$ .

$\frac{8 (x y^{3} w^{5})}{8 (w^{6} \cdot 3)}$

Cancel the common factor.

$\frac{8 (x y^{3} w^{5})}{8 (w^{6} \cdot 3)}$

Rewrite the expression.

$\frac{x y^{3} w^{5}}{w^{6} \cdot 3}$

Cancel the common factor of $w^{5}$ and $w^{6}$ .

Factor $w^{5}$ out of $x y^{3} w^{5}$ .

$\frac{w^{5} (x y^{3})}{w^{6} \cdot 3}$

Cancel the common factors.

Factor $w^{5}$ out of $w^{6} \cdot 3$ .

$\frac{w^{5} (x y^{3})}{w^{5} (w \cdot 3)}$

Cancel the common factor.

$\frac{w^{5} (x y^{3})}{w^{5} (w \cdot 3)}$

Rewrite the expression.

$\frac{x y^{3}}{w \cdot 3}$

Move $3$ to the left of $w$ .

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

Simplify (((2xy)/(w^2))^3)÷((24x^2)/(w^5))

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