Solve {left(18x^2y^5/27z^2right)}^2div{left(frac{10x^2{y}^3}{15z}right)}^3

$${ \left( \frac{ 18 { x }^{ 2 } { y }^{ 5 } }{ 27 { z }^{ 2 } } \right) }^{ 2 } \div { \left( \frac{ 10 { x }^{ 2 } { y }^{ 3 } }{ 15z } \right) }^{ 3 }$$

Evaluate

$$\frac{3y}{2zx^{2}}$$

Solution Steps

Cancel out 9 in both numerator and denominator.

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

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

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

Cancel out 5 in both numerator and denominator.

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

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

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

Divide \frac{\left(2x^{2}y^{5}\right)^{2}}{\left(3z^{2}\right)^{2}} by \frac{\left(2x^{2}y^{3}\right)^{3}}{\left(3z\right)^{3}} by multiplying \frac{\left(2x^{2}y^{5}\right)^{2}}{\left(3z^{2}\right)^{2}} by the reciprocal of \frac{\left(2x^{2}y^{3}\right)^{3}}{\left(3z\right)^{3}}.

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

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

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

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

$$\frac{2^{2}x^{4}\left(y^{5}\right)^{2}\times \left(3z\right)^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{2^{2}x^{4}y^{10}\times \left(3z\right)^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}y^{10}\times \left(3z\right)^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Expand \left(3z\right)^{3}.

$$\frac{4x^{4}y^{10}\times 3^{3}z^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{4x^{4}y^{10}\times 27z^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Multiply 4 and 27 to get 108.

$$\frac{108x^{4}y^{10}z^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{3^{2}\left(z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{3^{2}z^{4}\times \left(2x^{2}y^{3}\right)^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 2^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 2^{3}x^{6}\left(y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 2^{3}x^{6}y^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 8x^{6}y^{9}}$$

Multiply 9 and 8 to get 72.

$$\frac{108x^{4}y^{10}z^{3}}{72z^{4}x^{6}y^{9}}$$

Cancel out 36z^{3}x^{4}y^{9} in both numerator and denominator.

$$\frac{3y}{2zx^{2}}$$

Expand

$$\frac{3y}{2zx^{2}}$$

Solution Steps

Cancel out 9 in both numerator and denominator.

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

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

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

Cancel out 5 in both numerator and denominator.

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

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

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

Divide \frac{\left(2x^{2}y^{5}\right)^{2}}{\left(3z^{2}\right)^{2}} by \frac{\left(2x^{2}y^{3}\right)^{3}}{\left(3z\right)^{3}} by multiplying \frac{\left(2x^{2}y^{5}\right)^{2}}{\left(3z^{2}\right)^{2}} by the reciprocal of \frac{\left(2x^{2}y^{3}\right)^{3}}{\left(3z\right)^{3}}.

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

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

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

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

$$\frac{2^{2}x^{4}\left(y^{5}\right)^{2}\times \left(3z\right)^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{2^{2}x^{4}y^{10}\times \left(3z\right)^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}y^{10}\times \left(3z\right)^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Expand \left(3z\right)^{3}.

$$\frac{4x^{4}y^{10}\times 3^{3}z^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{4x^{4}y^{10}\times 27z^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

Multiply 4 and 27 to get 108.

$$\frac{108x^{4}y^{10}z^{3}}{\left(3z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{3^{2}\left(z^{2}\right)^{2}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{3^{2}z^{4}\times \left(2x^{2}y^{3}\right)^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times \left(2x^{2}y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 2^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 2^{3}x^{6}\left(y^{3}\right)^{3}}$$

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

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 2^{3}x^{6}y^{9}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{108x^{4}y^{10}z^{3}}{9z^{4}\times 8x^{6}y^{9}}$$

Multiply 9 and 8 to get 72.

$$\frac{108x^{4}y^{10}z^{3}}{72z^{4}x^{6}y^{9}}$$

Cancel out 36z^{3}x^{4}y^{9} in both numerator and denominator.

$$\frac{3y}{2zx^{2}}$$