Solve frac{(2x^{-4}y^5)^-2}{4x^4y^-5}

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

Evaluate

$$\frac{x^{4}}{16y^{5}}$$

Solution Steps

Expand \left(2x^{-4}y^{5}\right)^{-2}.

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

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

$$\frac{2^{-2}x^{8}\left(y^{5}\right)^{-2}}{4x^{4}y^{-5}}$$

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

$$\frac{2^{-2}x^{8}y^{-10}}{4x^{4}y^{-5}}$$

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

$$\frac{\frac{1}{4}x^{8}y^{-10}}{4x^{4}y^{-5}}$$

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

$$\frac{\frac{1}{4}y^{-10}x^{4}}{4y^{-5}}$$

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

$$\frac{\frac{1}{4}x^{4}}{4y^{5}}$$

Expand

$$\frac{x^{4}}{16y^{5}}$$

Solution Steps

Expand \left(2x^{-4}y^{5}\right)^{-2}.

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

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

$$\frac{2^{-2}x^{8}\left(y^{5}\right)^{-2}}{4x^{4}y^{-5}}$$

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

$$\frac{2^{-2}x^{8}y^{-10}}{4x^{4}y^{-5}}$$

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

$$\frac{\frac{1}{4}x^{8}y^{-10}}{4x^{4}y^{-5}}$$

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

$$\frac{\frac{1}{4}y^{-10}x^{4}}{4y^{-5}}$$

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

$$\frac{\frac{1}{4}x^{4}}{4y^{5}}$$