Solve (2x^{-1}y^{2}z^{5})^4(-3x^3yz^-3)^2

$$( 2 x ^ { - 1 } y ^ { 2 } z ^ { 5 } ) ^ { 4 } ( - 3 x ^ { 3 } y z ^ { - 3 } ) ^ { 2 }$$

Evaluate

$$144x^{2}y^{10}z^{14}$$

Solution Steps

Expand \left(2x^{-1}y^{2}z^{5}\right)^{4}.

$$2^{4}\left(x^{-1}\right)^{4}\left(y^{2}\right)^{4}\left(z^{5}\right)^{4}\left(-3x^{3}yz^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

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

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

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

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

$$2^{4}x^{-4}y^{8}z^{20}\left(-3x^{3}yz^{-3}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{-4}y^{8}z^{20}\left(-3x^{3}yz^{-3}\right)^{2}$$

Expand \left(-3x^{3}yz^{-3}\right)^{2}.

$$16x^{-4}y^{8}z^{20}\left(-3\right)^{2}\left(x^{3}\right)^{2}y^{2}\left(z^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$16x^{-4}y^{8}z^{20}\left(-3\right)^{2}x^{6}y^{2}\left(z^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$16x^{-4}y^{8}z^{20}\left(-3\right)^{2}x^{6}y^{2}z^{-6}$$

Calculate -3 to the power of 2 and get 9.

$$16x^{-4}y^{8}z^{20}\times 9x^{6}y^{2}z^{-6}$$

Multiply 16 and 9 to get 144.

$$144x^{-4}y^{8}z^{20}x^{6}y^{2}z^{-6}$$

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$144x^{2}y^{8}z^{20}y^{2}z^{-6}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$144x^{2}y^{10}z^{20}z^{-6}$$

To multiply powers of the same base, add their exponents. Add 20 and -6 to get 14.

$$144x^{2}y^{10}z^{14}$$

Expand

$$144x^{2}y^{10}z^{14}$$

Solution Steps

Expand \left(2x^{-1}y^{2}z^{5}\right)^{4}.

$$2^{4}\left(x^{-1}\right)^{4}\left(y^{2}\right)^{4}\left(z^{5}\right)^{4}\left(-3x^{3}yz^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

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

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

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

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

$$2^{4}x^{-4}y^{8}z^{20}\left(-3x^{3}yz^{-3}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{-4}y^{8}z^{20}\left(-3x^{3}yz^{-3}\right)^{2}$$

Expand \left(-3x^{3}yz^{-3}\right)^{2}.

$$16x^{-4}y^{8}z^{20}\left(-3\right)^{2}\left(x^{3}\right)^{2}y^{2}\left(z^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$16x^{-4}y^{8}z^{20}\left(-3\right)^{2}x^{6}y^{2}\left(z^{-3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$16x^{-4}y^{8}z^{20}\left(-3\right)^{2}x^{6}y^{2}z^{-6}$$

Calculate -3 to the power of 2 and get 9.

$$16x^{-4}y^{8}z^{20}\times 9x^{6}y^{2}z^{-6}$$

Multiply 16 and 9 to get 144.

$$144x^{-4}y^{8}z^{20}x^{6}y^{2}z^{-6}$$

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$144x^{2}y^{8}z^{20}y^{2}z^{-6}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$144x^{2}y^{10}z^{20}z^{-6}$$

To multiply powers of the same base, add their exponents. Add 20 and -6 to get 14.

$$144x^{2}y^{10}z^{14}$$