Solve ((3x^-5z^4)^4)^-1

$$( ( 3 x ^ { - 5 } z ^ { 4 } ) ^ { 4 } ) ^ { - 1 }$$

Evaluate

$$\frac{x^{20}}{81z^{16}}$$

Solution Steps

Expand \left(3x^{-5}z^{4}\right)^{4}.

$$\left(3^{4}\left(x^{-5}\right)^{4}\left(z^{4}\right)^{4}\right)^{-1}$$

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

$$\left(3^{4}x^{-20}\left(z^{4}\right)^{4}\right)^{-1}$$

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

$$\left(3^{4}x^{-20}z^{16}\right)^{-1}$$

Calculate 3 to the power of 4 and get 81.

$$\left(81x^{-20}z^{16}\right)^{-1}$$

Expand \left(81x^{-20}z^{16}\right)^{-1}.

$$81^{-1}\left(x^{-20}\right)^{-1}\left(z^{16}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -20 and -1 to get 20.

$$81^{-1}x^{20}\left(z^{16}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 16 and -1 to get -16.

$$81^{-1}x^{20}z^{-16}$$

Calculate 81 to the power of -1 and get \frac{1}{81}.

$$\frac{1}{81}x^{20}z^{-16}$$

Expand

$$\frac{x^{20}}{81z^{16}}$$

Solution Steps

Expand \left(3x^{-5}z^{4}\right)^{4}.

$$\left(3^{4}\left(x^{-5}\right)^{4}\left(z^{4}\right)^{4}\right)^{-1}$$

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

$$\left(3^{4}x^{-20}\left(z^{4}\right)^{4}\right)^{-1}$$

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

$$\left(3^{4}x^{-20}z^{16}\right)^{-1}$$

Calculate 3 to the power of 4 and get 81.

$$\left(81x^{-20}z^{16}\right)^{-1}$$

Expand \left(81x^{-20}z^{16}\right)^{-1}.

$$81^{-1}\left(x^{-20}\right)^{-1}\left(z^{16}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -20 and -1 to get 20.

$$81^{-1}x^{20}\left(z^{16}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 16 and -1 to get -16.

$$81^{-1}x^{20}z^{-16}$$

Calculate 81 to the power of -1 and get \frac{1}{81}.

$$\frac{1}{81}x^{20}z^{-16}$$