Solve (2x^{3}y^{2}z^2)^3(x^2z)^4

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

Evaluate

$$8y^{6}z^{10}x^{17}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$2^{3}x^{9}\left(y^{2}\right)^{3}\left(z^{2}\right)^{3}\left(x^{2}z\right)^{4}$$

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

$$2^{3}x^{9}y^{6}\left(z^{2}\right)^{3}\left(x^{2}z\right)^{4}$$

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

$$2^{3}x^{9}y^{6}z^{6}\left(x^{2}z\right)^{4}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{9}y^{6}z^{6}\left(x^{2}z\right)^{4}$$

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

$$8x^{9}y^{6}z^{6}\left(x^{2}\right)^{4}z^{4}$$

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

$$8x^{9}y^{6}z^{6}x^{8}z^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 8 to get 17.

$$8x^{17}y^{6}z^{6}z^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$8x^{17}y^{6}z^{10}$$

Expand

$$8y^{6}z^{10}x^{17}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$2^{3}x^{9}\left(y^{2}\right)^{3}\left(z^{2}\right)^{3}\left(x^{2}z\right)^{4}$$

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

$$2^{3}x^{9}y^{6}\left(z^{2}\right)^{3}\left(x^{2}z\right)^{4}$$

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

$$2^{3}x^{9}y^{6}z^{6}\left(x^{2}z\right)^{4}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{9}y^{6}z^{6}\left(x^{2}z\right)^{4}$$

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

$$8x^{9}y^{6}z^{6}\left(x^{2}\right)^{4}z^{4}$$

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

$$8x^{9}y^{6}z^{6}x^{8}z^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 8 to get 17.

$$8x^{17}y^{6}z^{6}z^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$8x^{17}y^{6}z^{10}$$