Solve (1^1/10y^4)^-4

$$( \frac { 1 ^ { 1 } } { 10 y ^ { 4 } } ) ^ { - 4 }$$

Evaluate

$$10000y^{16}$$

Solution Steps

Calculate 1 to the power of 1 and get 1.

$$\left(\frac{1}{10y^{4}}\right)^{-4}$$

To raise \frac{1}{10y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-4}}{\left(10y^{4}\right)^{-4}}$$

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

$$\frac{1}{\left(10y^{4}\right)^{-4}}$$

Expand \left(10y^{4}\right)^{-4}.

$$\frac{1}{10^{-4}\left(y^{4}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$\frac{1}{10^{-4}y^{-16}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{1}{\frac{1}{10000}y^{-16}}$$

Expand

$$10000y^{16}$$

Solution Steps

Calculate 1 to the power of 1 and get 1.

$$\left(\frac{1}{10y^{4}}\right)^{-4}$$

To raise \frac{1}{10y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-4}}{\left(10y^{4}\right)^{-4}}$$

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

$$\frac{1}{\left(10y^{4}\right)^{-4}}$$

Expand \left(10y^{4}\right)^{-4}.

$$\frac{1}{10^{-4}\left(y^{4}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$\frac{1}{10^{-4}y^{-16}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{1}{\frac{1}{10000}y^{-16}}$$