Solve (-frac{x^{0}*2y^-1}{x^-2y^4})^2

$$( - \frac { x ^ { 0 } \cdot 2 y ^ { - 1 } } { x ^ { - 2 } y ^ { 4 } } ) ^ { 2 }$$

Evaluate

$$\frac{4x^{4}}{y^{10}}$$

Solution Steps

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

$$\left(-\frac{2\times \frac{1}{y}x^{2}}{y^{4}}\right)^{2}$$

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

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

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

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

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

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

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

$$\frac{\left(2x^{2}\right)^{2}}{y^{10}}$$

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

$$\frac{2^{2}\left(x^{2}\right)^{2}}{y^{10}}$$

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

$$\frac{2^{2}x^{4}}{y^{10}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}}{y^{10}}$$

Expand

$$\frac{4x^{4}}{y^{10}}$$

Solution Steps

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

$$\left(-\frac{2\times \frac{1}{y}x^{2}}{y^{4}}\right)^{2}$$

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

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

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

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

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

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

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

$$\frac{\left(2x^{2}\right)^{2}}{y^{10}}$$

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

$$\frac{2^{2}\left(x^{2}\right)^{2}}{y^{10}}$$

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

$$\frac{2^{2}x^{4}}{y^{10}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{4}}{y^{10}}$$