Solve frac{(3x^{2}y^{2})^{3}x(x^4y)^6}{(xy^2)^2}

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

Evaluate

$$27y^{8}x^{29}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{6}y^{6}x\left(x^{4}y\right)^{6}}{\left(xy^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{27x^{7}y^{6}\left(x^{4}y\right)^{6}}{\left(xy^{2}\right)^{2}}$$

Expand \left(x^{4}y\right)^{6}.

$$\frac{27x^{7}y^{6}\left(x^{4}\right)^{6}y^{6}}{\left(xy^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{27x^{7}y^{6}x^{24}y^{6}}{\left(xy^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 7 and 24 to get 31.

$$\frac{27x^{31}y^{6}y^{6}}{\left(xy^{2}\right)^{2}}$$

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

$$\frac{27x^{31}y^{12}}{\left(xy^{2}\right)^{2}}$$

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

$$\frac{27x^{31}y^{12}}{x^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{27x^{31}y^{12}}{x^{2}y^{4}}$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$27y^{8}x^{29}$$

Expand

$$27y^{8}x^{29}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{6}y^{6}x\left(x^{4}y\right)^{6}}{\left(xy^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{27x^{7}y^{6}\left(x^{4}y\right)^{6}}{\left(xy^{2}\right)^{2}}$$

Expand \left(x^{4}y\right)^{6}.

$$\frac{27x^{7}y^{6}\left(x^{4}\right)^{6}y^{6}}{\left(xy^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{27x^{7}y^{6}x^{24}y^{6}}{\left(xy^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 7 and 24 to get 31.

$$\frac{27x^{31}y^{6}y^{6}}{\left(xy^{2}\right)^{2}}$$

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

$$\frac{27x^{31}y^{12}}{\left(xy^{2}\right)^{2}}$$

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

$$\frac{27x^{31}y^{12}}{x^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{27x^{31}y^{12}}{x^{2}y^{4}}$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$27y^{8}x^{29}$$