Solve (frac{-4x^{4}y^-2}{5x^-1y^4})^-4

$$( \frac { - 4 x ^ { 4 } y ^ { - 2 } } { 5 x ^ { - 1 } y ^ { 4 } } ) ^ { - 4 }$$

Evaluate

$$\frac{625y^{24}}{256x^{20}}$$

Solution Steps

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

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

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

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

To raise \frac{-4x^{5}}{5y^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and -4 to get -20.

$$\frac{\left(-4\right)^{-4}x^{-20}}{\left(5y^{6}\right)^{-4}}$$

Calculate -4 to the power of -4 and get \frac{1}{256}.

$$\frac{\frac{1}{256}x^{-20}}{\left(5y^{6}\right)^{-4}}$$

Expand \left(5y^{6}\right)^{-4}.

$$\frac{\frac{1}{256}x^{-20}}{5^{-4}\left(y^{6}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -4 to get -24.

$$\frac{\frac{1}{256}x^{-20}}{5^{-4}y^{-24}}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{\frac{1}{256}x^{-20}}{\frac{1}{625}y^{-24}}$$

Expand

$$\frac{625y^{24}}{256x^{20}}$$

Solution Steps

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

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

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

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

To raise \frac{-4x^{5}}{5y^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and -4 to get -20.

$$\frac{\left(-4\right)^{-4}x^{-20}}{\left(5y^{6}\right)^{-4}}$$

Calculate -4 to the power of -4 and get \frac{1}{256}.

$$\frac{\frac{1}{256}x^{-20}}{\left(5y^{6}\right)^{-4}}$$

Expand \left(5y^{6}\right)^{-4}.

$$\frac{\frac{1}{256}x^{-20}}{5^{-4}\left(y^{6}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -4 to get -24.

$$\frac{\frac{1}{256}x^{-20}}{5^{-4}y^{-24}}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{\frac{1}{256}x^{-20}}{\frac{1}{625}y^{-24}}$$