Solve (-2xy^2z)^3(2x^2yz)^2

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

Evaluate

$$-32z^{5}x^{7}y^{8}$$

Solution Steps

Expand \left(-2xy^{2}z\right)^{3}.

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

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

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply -8 and 4 to get -32.

$$-32x^{3}y^{6}z^{3}x^{4}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-32x^{7}y^{6}z^{3}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$-32x^{7}y^{8}z^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-32x^{7}y^{8}z^{5}$$

Expand

$$-32z^{5}x^{7}y^{8}$$

Solution Steps

Expand \left(-2xy^{2}z\right)^{3}.

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

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

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply -8 and 4 to get -32.

$$-32x^{3}y^{6}z^{3}x^{4}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-32x^{7}y^{6}z^{3}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$-32x^{7}y^{8}z^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-32x^{7}y^{8}z^{5}$$