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

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

Evaluate

$$-200z^{2}x^{12}y^{17}$$

Solution Steps

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

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

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

$$\left(-2\right)^{3}x^{6}\left(y^{3}\right)^{3}\times \left(5x^{3}y^{4}z\right)^{2}$$

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

$$\left(-2\right)^{3}x^{6}y^{9}\times \left(5x^{3}y^{4}z\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$-8x^{6}y^{9}\times \left(5x^{3}y^{4}z\right)^{2}$$

Expand \left(5x^{3}y^{4}z\right)^{2}.

$$-8x^{6}y^{9}\times 5^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}z^{2}$$

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

$$-8x^{6}y^{9}\times 5^{2}x^{6}\left(y^{4}\right)^{2}z^{2}$$

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

$$-8x^{6}y^{9}\times 5^{2}x^{6}y^{8}z^{2}$$

Calculate 5 to the power of 2 and get 25.

$$-8x^{6}y^{9}\times 25x^{6}y^{8}z^{2}$$

Multiply -8 and 25 to get -200.

$$-200x^{6}y^{9}x^{6}y^{8}z^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-200x^{12}y^{9}y^{8}z^{2}$$

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

$$-200x^{12}y^{17}z^{2}$$

Expand

$$-200z^{2}x^{12}y^{17}$$

Solution Steps

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

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

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

$$\left(-2\right)^{3}x^{6}\left(y^{3}\right)^{3}\times \left(5x^{3}y^{4}z\right)^{2}$$

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

$$\left(-2\right)^{3}x^{6}y^{9}\times \left(5x^{3}y^{4}z\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$-8x^{6}y^{9}\times \left(5x^{3}y^{4}z\right)^{2}$$

Expand \left(5x^{3}y^{4}z\right)^{2}.

$$-8x^{6}y^{9}\times 5^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}z^{2}$$

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

$$-8x^{6}y^{9}\times 5^{2}x^{6}\left(y^{4}\right)^{2}z^{2}$$

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

$$-8x^{6}y^{9}\times 5^{2}x^{6}y^{8}z^{2}$$

Calculate 5 to the power of 2 and get 25.

$$-8x^{6}y^{9}\times 25x^{6}y^{8}z^{2}$$

Multiply -8 and 25 to get -200.

$$-200x^{6}y^{9}x^{6}y^{8}z^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-200x^{12}y^{9}y^{8}z^{2}$$

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

$$-200x^{12}y^{17}z^{2}$$