Solve (4^-2/y^7x)^-4

$$( \frac { 4 ^ { - 2 } } { y ^ { 7 } x } ) ^ { - 4 }$$

Evaluate

$$65536x^{4}y^{28}$$

Solution Steps

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\left(\frac{\frac{1}{16}}{y^{7}x}\right)^{-4}$$

Express \frac{\frac{1}{16}}{y^{7}x} as a single fraction.

$$\left(\frac{1}{16y^{7}x}\right)^{-4}$$

To raise \frac{1}{16y^{7}x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-4}}{\left(16y^{7}x\right)^{-4}}$$

Calculate 1 to the power of -4 and get 1.

$$\frac{1}{\left(16y^{7}x\right)^{-4}}$$

Expand \left(16y^{7}x\right)^{-4}.

$$\frac{1}{16^{-4}\left(y^{7}\right)^{-4}x^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -4 to get -28.

$$\frac{1}{16^{-4}y^{-28}x^{-4}}$$

Calculate 16 to the power of -4 and get \frac{1}{65536}.

$$\frac{1}{\frac{1}{65536}y^{-28}x^{-4}}$$

Expand

$$65536x^{4}y^{28}$$

Solution Steps

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\left(\frac{\frac{1}{16}}{y^{7}x}\right)^{-4}$$

Express \frac{\frac{1}{16}}{y^{7}x} as a single fraction.

$$\left(\frac{1}{16y^{7}x}\right)^{-4}$$

To raise \frac{1}{16y^{7}x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-4}}{\left(16y^{7}x\right)^{-4}}$$

Calculate 1 to the power of -4 and get 1.

$$\frac{1}{\left(16y^{7}x\right)^{-4}}$$

Expand \left(16y^{7}x\right)^{-4}.

$$\frac{1}{16^{-4}\left(y^{7}\right)^{-4}x^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -4 to get -28.

$$\frac{1}{16^{-4}y^{-28}x^{-4}}$$

Calculate 16 to the power of -4 and get \frac{1}{65536}.

$$\frac{1}{\frac{1}{65536}y^{-28}x^{-4}}$$