Solve frac{(2x^{2}y)^{3}}{(10xy^3)^2}*(5xy^4)^3/4xy

$$\frac { ( 2 x ^ { 2 } y ) ^ { 3 } } { ( 10 x y ^ { 3 } ) ^ { 2 } } \times \frac { ( 5 x y ^ { 4 } ) ^ { 3 } } { 4 x y }$$

Evaluate

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

Solution Steps

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

$$\frac{2^{3}\left(x^{2}\right)^{3}y^{3}}{\left(10xy^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

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

$$\frac{2^{3}x^{6}y^{3}}{\left(10xy^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{6}y^{3}}{\left(10xy^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Expand \left(10xy^{3}\right)^{2}.

$$\frac{8x^{6}y^{3}}{10^{2}x^{2}\left(y^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

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

$$\frac{8x^{6}y^{3}}{10^{2}x^{2}y^{6}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{8x^{6}y^{3}}{100x^{2}y^{6}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Cancel out 4x^{2}y^{3} in both numerator and denominator.

$$\frac{2x^{4}}{25y^{3}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Expand \left(5xy^{4}\right)^{3}.

$$\frac{2x^{4}}{25y^{3}}\times \frac{5^{3}x^{3}\left(y^{4}\right)^{3}}{4xy}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{2x^{4}}{25y^{3}}\times \frac{5^{3}x^{3}y^{12}}{4xy}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{2x^{4}}{25y^{3}}\times \frac{125x^{3}y^{12}}{4xy}$$

Cancel out xy in both numerator and denominator.

$$\frac{2x^{4}}{25y^{3}}\times \frac{125x^{2}y^{11}}{4}$$

Multiply \frac{2x^{4}}{25y^{3}} times \frac{125x^{2}y^{11}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{4}\times 125x^{2}y^{11}}{25y^{3}\times 4}$$

Cancel out 2\times 25y^{3} in both numerator and denominator.

$$\frac{5x^{2}x^{4}y^{8}}{2}$$

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

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

Expand

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

Solution Steps

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

$$\frac{2^{3}\left(x^{2}\right)^{3}y^{3}}{\left(10xy^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

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

$$\frac{2^{3}x^{6}y^{3}}{\left(10xy^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{6}y^{3}}{\left(10xy^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Expand \left(10xy^{3}\right)^{2}.

$$\frac{8x^{6}y^{3}}{10^{2}x^{2}\left(y^{3}\right)^{2}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

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

$$\frac{8x^{6}y^{3}}{10^{2}x^{2}y^{6}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{8x^{6}y^{3}}{100x^{2}y^{6}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Cancel out 4x^{2}y^{3} in both numerator and denominator.

$$\frac{2x^{4}}{25y^{3}}\times \frac{\left(5xy^{4}\right)^{3}}{4xy}$$

Expand \left(5xy^{4}\right)^{3}.

$$\frac{2x^{4}}{25y^{3}}\times \frac{5^{3}x^{3}\left(y^{4}\right)^{3}}{4xy}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{2x^{4}}{25y^{3}}\times \frac{5^{3}x^{3}y^{12}}{4xy}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{2x^{4}}{25y^{3}}\times \frac{125x^{3}y^{12}}{4xy}$$

Cancel out xy in both numerator and denominator.

$$\frac{2x^{4}}{25y^{3}}\times \frac{125x^{2}y^{11}}{4}$$

Multiply \frac{2x^{4}}{25y^{3}} times \frac{125x^{2}y^{11}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{4}\times 125x^{2}y^{11}}{25y^{3}\times 4}$$

Cancel out 2\times 25y^{3} in both numerator and denominator.

$$\frac{5x^{2}x^{4}y^{8}}{2}$$

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

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