Solve (-5/x)^2*(2x^4/y^3)^2

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

Evaluate

$$100\times \left(\frac{x}{y}\right)^{6}$$

Solution Steps

Calculate -\frac{5}{x} to the power of 2 and get \left(\frac{5}{x}\right)^{2}.

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

To raise \frac{2x^{4}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{5^{2}}{x^{2}}\times \frac{4x^{8}}{y^{6}}$$

Multiply \frac{5^{2}}{x^{2}} times \frac{4x^{8}}{y^{6}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5^{2}\times 4x^{8}}{x^{2}y^{6}}$$

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

$$\frac{4\times 5^{2}x^{6}}{y^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4\times 25x^{6}}{y^{6}}$$

Multiply 4 and 25 to get 100.

$$\frac{100x^{6}}{y^{6}}$$

Expand

$$100\times \left(\frac{x}{y}\right)^{6}$$

Solution Steps

Calculate -\frac{5}{x} to the power of 2 and get \left(\frac{5}{x}\right)^{2}.

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

To raise \frac{2x^{4}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{5^{2}}{x^{2}}\times \frac{4x^{8}}{y^{6}}$$

Multiply \frac{5^{2}}{x^{2}} times \frac{4x^{8}}{y^{6}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5^{2}\times 4x^{8}}{x^{2}y^{6}}$$

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

$$\frac{4\times 5^{2}x^{6}}{y^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4\times 25x^{6}}{y^{6}}$$

Multiply 4 and 25 to get 100.

$$\frac{100x^{6}}{y^{6}}$$