Solve (frac{18x^{2}y^{5}}{27x^2})^2*(10x^2y^3/15x)

$$( \frac { 18 x ^ { 2 } y ^ { 5 } } { 27 x ^ { 2 } } ) ^ { 2 } \cdot ( \frac { 10 x ^ { 2 } y ^ { 3 } } { 15 x } )$$

Evaluate

$$\frac{8xy^{13}}{27}$$

Solution Steps

Cancel out 9x^{2} in both numerator and denominator.

$$\left(\frac{2y^{5}}{3}\right)^{2}\times \frac{10x^{2}y^{3}}{15x}$$

To raise \frac{2y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2y^{5}\right)^{2}}{3^{2}}\times \frac{10x^{2}y^{3}}{15x}$$

Cancel out 5x in both numerator and denominator.

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

Multiply \frac{\left(2y^{5}\right)^{2}}{3^{2}} times \frac{2xy^{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Expand \left(2y^{5}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{2^{2}y^{10}\times 2xy^{3}}{3^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4y^{10}\times 2xy^{3}}{3^{3}}$$

Multiply 4 and 2 to get 8.

$$\frac{8y^{10}xy^{3}}{3^{3}}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$\frac{8y^{13}x}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8y^{13}x}{27}$$

Expand

$$\frac{8xy^{13}}{27}$$

Solution Steps

Cancel out 9x^{2} in both numerator and denominator.

$$\left(\frac{2y^{5}}{3}\right)^{2}\times \frac{10x^{2}y^{3}}{15x}$$

To raise \frac{2y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2y^{5}\right)^{2}}{3^{2}}\times \frac{10x^{2}y^{3}}{15x}$$

Cancel out 5x in both numerator and denominator.

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

Multiply \frac{\left(2y^{5}\right)^{2}}{3^{2}} times \frac{2xy^{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Expand \left(2y^{5}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{2^{2}y^{10}\times 2xy^{3}}{3^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4y^{10}\times 2xy^{3}}{3^{3}}$$

Multiply 4 and 2 to get 8.

$$\frac{8y^{10}xy^{3}}{3^{3}}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$\frac{8y^{13}x}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8y^{13}x}{27}$$