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

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

Evaluate

$$18y^{5}$$

Solution Steps

Expand \left(12x^{2}y^{6}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

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

Calculate 12 to the power of 2 and get 144.

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

Cancel out 8x^{4}y^{7} in both numerator and denominator.

$$18y^{5}$$

Expand

$$18y^{5}$$

Solution Steps

Expand \left(12x^{2}y^{6}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

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

Calculate 12 to the power of 2 and get 144.

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

Cancel out 8x^{4}y^{7} in both numerator and denominator.

$$18y^{5}$$