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

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

Evaluate

$$54z^{3}x^{7}y^{12}$$

Solution Steps

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

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

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

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

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

$$3^{3}x^{6}y^{9}\times 2xy^{3}z^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{6}y^{9}\times 2xy^{3}z^{3}$$

Multiply 27 and 2 to get 54.

$$54x^{6}y^{9}xy^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$54x^{7}y^{9}y^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$54x^{7}y^{12}z^{3}$$

Expand

$$54z^{3}x^{7}y^{12}$$

Solution Steps

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

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

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

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

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

$$3^{3}x^{6}y^{9}\times 2xy^{3}z^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{6}y^{9}\times 2xy^{3}z^{3}$$

Multiply 27 and 2 to get 54.

$$54x^{6}y^{9}xy^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$54x^{7}y^{9}y^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$54x^{7}y^{12}z^{3}$$