Solve (-3x^{-4}y^{2}z)^{-2}(6x^5y^-4z^0)^2

$$( - 3 x ^ { - 4 } y ^ { 2 } z ) ^ { - 2 } ( 6 x ^ { 5 } y ^ { - 4 } z ^ { 0 } ) ^ { 2 }$$

Evaluate

$$\frac{4x^{18}}{z^{2}y^{12}}$$

Solution Steps

Expand \left(-3x^{-4}y^{2}z\right)^{-2}.

$$\left(-3\right)^{-2}\left(x^{-4}\right)^{-2}\left(y^{2}\right)^{-2}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

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

$$\left(-3\right)^{-2}x^{8}\left(y^{2}\right)^{-2}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

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

$$\left(-3\right)^{-2}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

Calculate z to the power of 0 and get 1.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}\times 1\right)^{2}$$

Multiply 6 and 1 to get 6.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}\right)^{2}$$

Expand \left(6x^{5}y^{-4}\right)^{2}.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 6^{2}\left(x^{5}\right)^{2}\left(y^{-4}\right)^{2}$$

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

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 6^{2}x^{10}\left(y^{-4}\right)^{2}$$

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

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 6^{2}x^{10}y^{-8}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 36x^{10}y^{-8}$$

Multiply \frac{1}{9} and 36 to get 4.

$$4x^{8}y^{-4}z^{-2}x^{10}y^{-8}$$

To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.

$$4x^{18}y^{-4}z^{-2}y^{-8}$$

To multiply powers of the same base, add their exponents. Add -4 and -8 to get -12.

$$4x^{18}y^{-12}z^{-2}$$

Expand

$$\frac{4x^{18}}{z^{2}y^{12}}$$

Solution Steps

Expand \left(-3x^{-4}y^{2}z\right)^{-2}.

$$\left(-3\right)^{-2}\left(x^{-4}\right)^{-2}\left(y^{2}\right)^{-2}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

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

$$\left(-3\right)^{-2}x^{8}\left(y^{2}\right)^{-2}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

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

$$\left(-3\right)^{-2}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}z^{0}\right)^{2}$$

Calculate z to the power of 0 and get 1.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}\times 1\right)^{2}$$

Multiply 6 and 1 to get 6.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times \left(6x^{5}y^{-4}\right)^{2}$$

Expand \left(6x^{5}y^{-4}\right)^{2}.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 6^{2}\left(x^{5}\right)^{2}\left(y^{-4}\right)^{2}$$

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

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 6^{2}x^{10}\left(y^{-4}\right)^{2}$$

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

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 6^{2}x^{10}y^{-8}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1}{9}x^{8}y^{-4}z^{-2}\times 36x^{10}y^{-8}$$

Multiply \frac{1}{9} and 36 to get 4.

$$4x^{8}y^{-4}z^{-2}x^{10}y^{-8}$$

To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.

$$4x^{18}y^{-4}z^{-2}y^{-8}$$

To multiply powers of the same base, add their exponents. Add -4 and -8 to get -12.

$$4x^{18}y^{-12}z^{-2}$$