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

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

Evaluate

$$243z^{2}x^{6}y^{15}$$

Solution Steps

Expand \left(-3xy^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-3\right)^{4}x^{4}y^{12}\times 3x^{2}y^{3}z^{2}$$

Calculate -3 to the power of 4 and get 81.

$$81x^{4}y^{12}\times 3x^{2}y^{3}z^{2}$$

Multiply 81 and 3 to get 243.

$$243x^{4}y^{12}x^{2}y^{3}z^{2}$$

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

$$243x^{6}y^{12}y^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$243x^{6}y^{15}z^{2}$$

Expand

$$243z^{2}x^{6}y^{15}$$

Solution Steps

Expand \left(-3xy^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-3\right)^{4}x^{4}y^{12}\times 3x^{2}y^{3}z^{2}$$

Calculate -3 to the power of 4 and get 81.

$$81x^{4}y^{12}\times 3x^{2}y^{3}z^{2}$$

Multiply 81 and 3 to get 243.

$$243x^{4}y^{12}x^{2}y^{3}z^{2}$$

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

$$243x^{6}y^{12}y^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$243x^{6}y^{15}z^{2}$$