Simplify ((12x^2y^6)^2)/(8x^4y^7)

$\frac{{(12 x^{2} y^{6})}^{2}}{8 x^{4} y^{7}}$

Step 1

Simplify the numerator.

Apply the product rule to $12 x^{2} y^{6}$ .

$\frac{{(12 x^{2})}^{2} {(y^{6})}^{2}}{8 x^{4} y^{7}}$

Apply the product rule to $12 x^{2}$ .

$\frac{12^{2} {(x^{2})}^{2} {(y^{6})}^{2}}{8 x^{4} y^{7}}$

Raise $12$ to the power of $2$ .

$\frac{144 {(x^{2})}^{2} {(y^{6})}^{2}}{8 x^{4} y^{7}}$

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

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

$\frac{144 x^{2 \cdot 2} {(y^{6})}^{2}}{8 x^{4} y^{7}}$

Multiply $2$ by $2$ .

$\frac{144 x^{4} {(y^{6})}^{2}}{8 x^{4} y^{7}}$

Multiply the exponents in ${(y^{6})}^{2}$ .

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

$\frac{144 x^{4} y^{6 \cdot 2}}{8 x^{4} y^{7}}$

Multiply $6$ by $2$ .

$\frac{144 x^{4} y^{12}}{8 x^{4} y^{7}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $144$ and $8$ .

Factor $8$ out of $144 x^{4} y^{12}$ .

$\frac{8 (18 x^{4} y^{12})}{8 x^{4} y^{7}}$

Cancel the common factors.

Factor $8$ out of $8 x^{4} y^{7}$ .

$\frac{8 (18 x^{4} y^{12})}{8 (x^{4} y^{7})}$

Cancel the common factor.

$\frac{8 (18 x^{4} y^{12})}{8 (x^{4} y^{7})}$

Rewrite the expression.

$\frac{18 x^{4} y^{12}}{x^{4} y^{7}}$

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

Cancel the common factor.

$\frac{18 x^{4} y^{12}}{x^{4} y^{7}}$

Rewrite the expression.

$\frac{18 y^{12}}{y^{7}}$

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

Factor $y^{7}$ out of $18 y^{12}$ .

$\frac{y^{7} (18 y^{5})}{y^{7}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{7} (18 y^{5})}{y^{7} \cdot 1}$

Cancel the common factor.

$\frac{y^{7} (18 y^{5})}{y^{7} \cdot 1}$

Rewrite the expression.

$\frac{18 y^{5}}{1}$

Divide $18 y^{5}$ by $1$ .

$18 y^{5}$

Simplify ((12x^2y^6)^2)/(8x^4y^7)

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