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

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

Evaluate

$$9z^{11}\left(xy\right)^{6}$$

Solution Steps

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

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

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

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

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

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

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

$$3^{2}x^{4}y^{6}z^{8}x^{2}z^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}y^{6}z^{8}x^{2}z^{3}$$

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

$$9x^{6}y^{6}z^{8}z^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$9x^{6}y^{6}z^{11}$$

Expand

$$9z^{11}\left(xy\right)^{6}$$

Solution Steps

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

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

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

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

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

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

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

$$3^{2}x^{4}y^{6}z^{8}x^{2}z^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}y^{6}z^{8}x^{2}z^{3}$$

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

$$9x^{6}y^{6}z^{8}z^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$9x^{6}y^{6}z^{11}$$