Solve (2/3xy)^12:(2/3)^10

$$( \frac { 2 } { 3 } x y ) ^ { 12 } : ( \frac { 2 } { 3 } ) ^ { 10 }$$

Evaluate

$$\frac{4\left(xy\right)^{12}}{9}$$

Solution Steps

Expand \left(\frac{2}{3}xy\right)^{12}.

$$\frac{\left(\frac{2}{3}\right)^{12}x^{12}y^{12}}{\left(\frac{2}{3}\right)^{10}}$$

Calculate \frac{2}{3} to the power of 12 and get \frac{4096}{531441}.

$$\frac{\frac{4096}{531441}x^{12}y^{12}}{\left(\frac{2}{3}\right)^{10}}$$

Calculate \frac{2}{3} to the power of 10 and get \frac{1024}{59049}.

$$\frac{\frac{4096}{531441}x^{12}y^{12}}{\frac{1024}{59049}}$$

Divide \frac{4096}{531441}x^{12}y^{12} by \frac{1024}{59049} by multiplying \frac{4096}{531441}x^{12}y^{12} by the reciprocal of \frac{1024}{59049}.

$$\frac{\frac{4096}{531441}x^{12}y^{12}\times 59049}{1024}$$

Multiply \frac{4096}{531441} and 59049 to get \frac{4096}{9}.

$$\frac{\frac{4096}{9}x^{12}y^{12}}{1024}$$

Divide \frac{4096}{9}x^{12}y^{12} by 1024 to get \frac{4}{9}x^{12}y^{12}.

$$\frac{4}{9}x^{12}y^{12}$$

Expand

$$\frac{4\left(xy\right)^{12}}{9}$$

Solution Steps

Expand \left(\frac{2}{3}xy\right)^{12}.

$$\frac{\left(\frac{2}{3}\right)^{12}x^{12}y^{12}}{\left(\frac{2}{3}\right)^{10}}$$

Calculate \frac{2}{3} to the power of 12 and get \frac{4096}{531441}.

$$\frac{\frac{4096}{531441}x^{12}y^{12}}{\left(\frac{2}{3}\right)^{10}}$$

Calculate \frac{2}{3} to the power of 10 and get \frac{1024}{59049}.

$$\frac{\frac{4096}{531441}x^{12}y^{12}}{\frac{1024}{59049}}$$

Divide \frac{4096}{531441}x^{12}y^{12} by \frac{1024}{59049} by multiplying \frac{4096}{531441}x^{12}y^{12} by the reciprocal of \frac{1024}{59049}.

$$\frac{\frac{4096}{531441}x^{12}y^{12}\times 59049}{1024}$$

Multiply \frac{4096}{531441} and 59049 to get \frac{4096}{9}.

$$\frac{\frac{4096}{9}x^{12}y^{12}}{1024}$$

Divide \frac{4096}{9}x^{12}y^{12} by 1024 to get \frac{4}{9}x^{12}y^{12}.

$$\frac{4}{9}x^{12}y^{12}$$