Simplify ((2x^2)^3(3y^4)^3)/(9x^4y^7)-18x^2y^5

$\frac{{(2 x^{2})}^{3} {(3 y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

Simplify each term.

Simplify the numerator.

Apply the product rule to $2 x^{2}$ .

$\frac{2^{3} {(x^{2})}^{3} {(3 y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

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

$\frac{2^{3} {(x^{2})}^{3} \cdot 3^{3} {(y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

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

$\frac{8 {(x^{2})}^{3} \cdot 3^{3} {(y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

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

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

$\frac{8 x^{2 \cdot 3} \cdot 3^{3} {(y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

Multiply $2$ by $3$ .

$\frac{8 x^{6} \cdot 3^{3} {(y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

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

$\frac{8 x^{6} \cdot 27 {(y^{4})}^{3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

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

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

$\frac{8 x^{6} \cdot 27 y^{4 \cdot 3}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

Multiply $4$ by $3$ .

$\frac{8 x^{6} \cdot 27 y^{12}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

Multiply $27$ by $8$ .

$\frac{216 x^{6} y^{12}}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

Cancel the common factor of $216$ and $9$ .

Factor $9$ out of $216 x^{6} y^{12}$ .

$\frac{9 (24 x^{6} y^{12})}{9 x^{4} y^{7}} - 18 x^{2} y^{5}$

Cancel the common factors.

Factor $9$ out of $9 x^{4} y^{7}$ .

$\frac{9 (24 x^{6} y^{12})}{9 (x^{4} y^{7})} - 18 x^{2} y^{5}$

Cancel the common factor.

$\frac{9 (24 x^{6} y^{12})}{9 (x^{4} y^{7})} - 18 x^{2} y^{5}$

Rewrite the expression.

$\frac{24 x^{6} y^{12}}{x^{4} y^{7}} - 18 x^{2} y^{5}$

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $24 x^{6} y^{12}$ .

$\frac{x^{4} (24 x^{2} y^{12})}{x^{4} y^{7}} - 18 x^{2} y^{5}$

Cancel the common factors.

Factor $x^{4}$ out of $x^{4} y^{7}$ .

$\frac{x^{4} (24 x^{2} y^{12})}{x^{4} (y^{7})} - 18 x^{2} y^{5}$

Cancel the common factor.

$\frac{x^{4} (24 x^{2} y^{12})}{x^{4} y^{7}} - 18 x^{2} y^{5}$

Rewrite the expression.

$\frac{24 x^{2} y^{12}}{y^{7}} - 18 x^{2} y^{5}$

Cancel the common factor of $y^{12}$ and $y^{7}$ .

Factor $y^{7}$ out of $24 x^{2} y^{12}$ .

$\frac{y^{7} (24 x^{2} y^{5})}{y^{7}} - 18 x^{2} y^{5}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{7} (24 x^{2} y^{5})}{y^{7} \cdot 1} - 18 x^{2} y^{5}$

Cancel the common factor.

$\frac{y^{7} (24 x^{2} y^{5})}{y^{7} \cdot 1} - 18 x^{2} y^{5}$

Rewrite the expression.

$\frac{24 x^{2} y^{5}}{1} - 18 x^{2} y^{5}$

Divide $24 x^{2} y^{5}$ by $1$ .

$24 x^{2} y^{5} - 18 x^{2} y^{5}$

Subtract $18 x^{2} y^{5}$ from $24 x^{2} y^{5}$ .

$6 x^{2} y^{5}$

Simplify ((2x^2)^3(3y^4)^3)/(9x^4y^7)-18x^2y^5

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