Simplify ((-6x^2y^3)^4)/(8x^9y^7*3xy^5)

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

Multiply $x^{9}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{9}$ .

Raise $x$ to the power of $1$ .

$\frac{{(- 6 x^{2} y^{3})}^{4}}{8 (x^{1} x^{9}) y^{7} \cdot (3 y^{5})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(- 6 x^{2} y^{3})}^{4}}{8 x^{1 + 9} y^{7} \cdot (3 y^{5})}$

Add $1$ and $9$ .

$\frac{{(- 6 x^{2} y^{3})}^{4}}{8 x^{10} y^{7} \cdot (3 y^{5})}$

Multiply $y^{7}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$\frac{{(- 6 x^{2} y^{3})}^{4}}{8 x^{10} (y^{5} y^{7}) \cdot 3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(- 6 x^{2} y^{3})}^{4}}{8 x^{10} y^{5 + 7} \cdot 3}$

Add $5$ and $7$ .

$\frac{{(- 6 x^{2} y^{3})}^{4}}{8 x^{10} y^{12} \cdot 3}$

Simplify the numerator.

Apply the product rule to $- 6 x^{2} y^{3}$ .

$\frac{{(- 6 x^{2})}^{4} {(y^{3})}^{4}}{8 x^{10} y^{12} \cdot 3}$

Apply the product rule to $- 6 x^{2}$ .

$\frac{{(- 6)}^{4} {(x^{2})}^{4} {(y^{3})}^{4}}{8 x^{10} y^{12} \cdot 3}$

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

$\frac{1296 {(x^{2})}^{4} {(y^{3})}^{4}}{8 x^{10} y^{12} \cdot 3}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$\frac{1296 x^{2 \cdot 4} {(y^{3})}^{4}}{8 x^{10} y^{12} \cdot 3}$

Multiply $2$ by $4$ .

$\frac{1296 x^{8} {(y^{3})}^{4}}{8 x^{10} y^{12} \cdot 3}$

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

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

$\frac{1296 x^{8} y^{3 \cdot 4}}{8 x^{10} y^{12} \cdot 3}$

Multiply $3$ by $4$ .

$\frac{1296 x^{8} y^{12}}{8 x^{10} y^{12} \cdot 3}$

Reduce the expression by cancelling the common factors.

Multiply $3$ by $8$ .

$\frac{1296 x^{8} y^{12}}{24 x^{10} y^{12}}$

Cancel the common factor of $1296$ and $24$ .

Factor $24$ out of $1296 x^{8} y^{12}$ .

$\frac{24 (54 x^{8} y^{12})}{24 x^{10} y^{12}}$

Cancel the common factors.

Factor $24$ out of $24 x^{10} y^{12}$ .

$\frac{24 (54 x^{8} y^{12})}{24 (x^{10} y^{12})}$

Cancel the common factor.

$\frac{24 (54 x^{8} y^{12})}{24 (x^{10} y^{12})}$

Rewrite the expression.

$\frac{54 x^{8} y^{12}}{x^{10} y^{12}}$

Cancel the common factor of $x^{8}$ and $x^{10}$ .

Factor $x^{8}$ out of $54 x^{8} y^{12}$ .

$\frac{x^{8} (54 y^{12})}{x^{10} y^{12}}$

Cancel the common factors.

Factor $x^{8}$ out of $x^{10} y^{12}$ .

$\frac{x^{8} (54 y^{12})}{x^{8} (x^{2} y^{12})}$

Cancel the common factor.

$\frac{x^{8} (54 y^{12})}{x^{8} (x^{2} y^{12})}$

Rewrite the expression.

$\frac{54 y^{12}}{x^{2} y^{12}}$

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

Cancel the common factor.

$\frac{54 y^{12}}{x^{2} y^{12}}$

Rewrite the expression.

$\frac{54}{x^{2}}$

Simplify ((-6x^2y^3)^4)/(8x^9y^7*3xy^5)

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