Solve (frac{x^{-1}y^-3}{2x^0y^-5})^-2

$$( \frac { x ^ { - 1 } y ^ { - 3 } } { 2 x ^ { 0 } y ^ { - 5 } } ) ^ { - 2 }$$

Evaluate

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

Solution Steps

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

$$\left(\frac{\frac{1}{x}y^{2}}{2x^{0}}\right)^{-2}$$

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

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

Calculate x to the power of 1 and get x.

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

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

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

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

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

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

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{y^{-4}}{\frac{1}{4}x^{-2}}$$

Expand

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

Solution Steps

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

$$\left(\frac{\frac{1}{x}y^{2}}{2x^{0}}\right)^{-2}$$

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

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

Calculate x to the power of 1 and get x.

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

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

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

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

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

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

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{y^{-4}}{\frac{1}{4}x^{-2}}$$