Solve (frac{5x^{-4}y^{3}}{2x^{2}y^0})^2*(4xy/y^3)^2

$$( \frac { 5 x ^ { - 4 } y ^ { 3 } } { 2 x ^ { 2 } y ^ { 0 } } ) ^ { 2 } \cdot ( \frac { 4 x y } { y ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{100y^{2}}{x^{10}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

To raise \frac{5y^{3}}{2x^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

Cancel out y in both numerator and denominator.

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

To raise \frac{4x}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(5y^{3}\right)^{2}}{\left(2x^{6}\right)^{2}} times \frac{\left(4x\right)^{2}}{\left(y^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Expand \left(5y^{3}\right)^{2}.

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

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{25y^{6}\times \left(4x\right)^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Expand \left(4x\right)^{2}.

$$\frac{25y^{6}\times 4^{2}x^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{25y^{6}\times 16x^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Multiply 25 and 16 to get 400.

$$\frac{400y^{6}x^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Expand \left(2x^{6}\right)^{2}.

$$\frac{400y^{6}x^{2}}{2^{2}\left(x^{6}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{400y^{6}x^{2}}{2^{2}x^{12}y^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{400y^{6}x^{2}}{4x^{12}y^{4}}$$

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

$$\frac{100y^{2}}{x^{10}}$$

Expand

$$\frac{100y^{2}}{x^{10}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

To raise \frac{5y^{3}}{2x^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

Cancel out y in both numerator and denominator.

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

To raise \frac{4x}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(5y^{3}\right)^{2}}{\left(2x^{6}\right)^{2}} times \frac{\left(4x\right)^{2}}{\left(y^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Expand \left(5y^{3}\right)^{2}.

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

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{25y^{6}\times \left(4x\right)^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Expand \left(4x\right)^{2}.

$$\frac{25y^{6}\times 4^{2}x^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{25y^{6}\times 16x^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Multiply 25 and 16 to get 400.

$$\frac{400y^{6}x^{2}}{\left(2x^{6}\right)^{2}y^{4}}$$

Expand \left(2x^{6}\right)^{2}.

$$\frac{400y^{6}x^{2}}{2^{2}\left(x^{6}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{400y^{6}x^{2}}{2^{2}x^{12}y^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{400y^{6}x^{2}}{4x^{12}y^{4}}$$

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

$$\frac{100y^{2}}{x^{10}}$$