Simplify ((8x^6y^6)/(4x^3y^12))^2

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

Step 1

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 x^{6} y^{6}$ .

${(\frac{4 (2 x^{6} y^{6})}{4 x^{3} y^{12}})}^{2}$

Cancel the common factors.

Factor $4$ out of $4 x^{3} y^{12}$ .

${(\frac{4 (2 x^{6} y^{6})}{4 (x^{3} y^{12})})}^{2}$

Cancel the common factor.

${(\frac{4 (2 x^{6} y^{6})}{4 (x^{3} y^{12})})}^{2}$

Rewrite the expression.

${(\frac{2 x^{6} y^{6}}{x^{3} y^{12}})}^{2}$

Step 2

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

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

${(\frac{x^{3} (2 x^{3} y^{6})}{x^{3} y^{12}})}^{2}$

Cancel the common factors.

Factor $x^{3}$ out of $x^{3} y^{12}$ .

${(\frac{x^{3} (2 x^{3} y^{6})}{x^{3} (y^{12})})}^{2}$

Cancel the common factor.

${(\frac{x^{3} (2 x^{3} y^{6})}{x^{3} y^{12}})}^{2}$

Rewrite the expression.

${(\frac{2 x^{3} y^{6}}{y^{12}})}^{2}$

Step 3

Cancel the common factor of $y^{6}$ and $y^{12}$ .

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

${(\frac{y^{6} (2 x^{3})}{y^{12}})}^{2}$

Cancel the common factors.

Factor $y^{6}$ out of $y^{12}$ .

${(\frac{y^{6} (2 x^{3})}{y^{6} y^{6}})}^{2}$

Cancel the common factor.

${(\frac{y^{6} (2 x^{3})}{y^{6} y^{6}})}^{2}$

Rewrite the expression.

${(\frac{2 x^{3}}{y^{6}})}^{2}$

Step 4

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

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

$\frac{{(2 x^{3})}^{2}}{{(y^{6})}^{2}}$

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

$\frac{2^{2} {(x^{3})}^{2}}{{(y^{6})}^{2}}$

Step 5

Simplify the numerator.

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

$\frac{4 {(x^{3})}^{2}}{{(y^{6})}^{2}}$

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

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

$\frac{4 x^{3 \cdot 2}}{{(y^{6})}^{2}}$

Multiply $3$ by $2$ .

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

Step 6

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

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

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

Multiply $6$ by $2$ .

$\frac{4 x^{6}}{y^{12}}$

Simplify ((8x^6y^6)/(4x^3y^12))^2

Related Questions

Support LCMGCF.com by disabling your adblocker.