Solve frac{(2xy^{2})^{3}x(x^{3}y^{2})^{3}}{2x^4y^11x^2y^4}

$$\frac { ( 2 x y ^ { 2 } ) ^ { 3 } x ( x ^ { 3 } y ^ { 2 } ) ^ { 3 } } { 2 x ^ { 4 } y ^ { 11 } x ^ { 2 } y ^ { 4 } }$$

Evaluate

$$\frac{4x^{7}}{y^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\left(2xy^{2}\right)^{3}x\left(x^{3}y^{2}\right)^{3}}{2x^{6}y^{11}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 11 and 4 to get 15.

$$\frac{\left(2xy^{2}\right)^{3}x\left(x^{3}y^{2}\right)^{3}}{2x^{6}y^{15}}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(2xy^{2}\right)^{3}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

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

$$\frac{2^{3}x^{3}\left(y^{2}\right)^{3}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{2^{3}x^{3}y^{6}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}y^{6}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

Expand \left(y^{2}x^{3}\right)^{3}.

$$\frac{8x^{3}y^{6}\left(y^{2}\right)^{3}\left(x^{3}\right)^{3}}{2x^{5}y^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{8x^{3}y^{6}y^{6}\left(x^{3}\right)^{3}}{2x^{5}y^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{8x^{3}y^{6}y^{6}x^{9}}{2x^{5}y^{15}}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{8x^{3}y^{12}x^{9}}{2x^{5}y^{15}}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{8x^{12}y^{12}}{2x^{5}y^{15}}$$

Cancel out 2x^{5}y^{12} in both numerator and denominator.

$$\frac{4x^{7}}{y^{3}}$$

Expand

$$\frac{4x^{7}}{y^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\left(2xy^{2}\right)^{3}x\left(x^{3}y^{2}\right)^{3}}{2x^{6}y^{11}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 11 and 4 to get 15.

$$\frac{\left(2xy^{2}\right)^{3}x\left(x^{3}y^{2}\right)^{3}}{2x^{6}y^{15}}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(2xy^{2}\right)^{3}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

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

$$\frac{2^{3}x^{3}\left(y^{2}\right)^{3}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{2^{3}x^{3}y^{6}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}y^{6}\left(y^{2}x^{3}\right)^{3}}{2x^{5}y^{15}}$$

Expand \left(y^{2}x^{3}\right)^{3}.

$$\frac{8x^{3}y^{6}\left(y^{2}\right)^{3}\left(x^{3}\right)^{3}}{2x^{5}y^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{8x^{3}y^{6}y^{6}\left(x^{3}\right)^{3}}{2x^{5}y^{15}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{8x^{3}y^{6}y^{6}x^{9}}{2x^{5}y^{15}}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{8x^{3}y^{12}x^{9}}{2x^{5}y^{15}}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{8x^{12}y^{12}}{2x^{5}y^{15}}$$

Cancel out 2x^{5}y^{12} in both numerator and denominator.

$$\frac{4x^{7}}{y^{3}}$$