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

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

Evaluate

$$-24z^{2}y^{7}x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

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

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

$$\left(-2x^{3}y^{2}\right)^{3}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$\left(-2\right)^{3}\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$\left(-2\right)^{3}x^{9}\left(y^{2}\right)^{3}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$\left(-2\right)^{3}x^{9}y^{6}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$-8x^{9}y^{6}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

Multiply -8 and 5 to get -40.

$$-40x^{9}y^{6}yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$-40x^{9}y^{7}z^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

Multiply 4 and -4 to get -16.

$$-40x^{9}y^{7}z^{2}-\left(-16x^{9}y^{7}z^{2}\right)$$

The opposite of -16x^{9}y^{7}z^{2} is 16x^{9}y^{7}z^{2}.

$$-40x^{9}y^{7}z^{2}+16x^{9}y^{7}z^{2}$$

Combine -40x^{9}y^{7}z^{2} and 16x^{9}y^{7}z^{2} to get -24x^{9}y^{7}z^{2}.

$$-24x^{9}y^{7}z^{2}$$

Expand

$$-24z^{2}y^{7}x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

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

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

$$\left(-2x^{3}y^{2}\right)^{3}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$\left(-2\right)^{3}\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$\left(-2\right)^{3}x^{9}\left(y^{2}\right)^{3}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$\left(-2\right)^{3}x^{9}y^{6}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$-8x^{9}y^{6}\times 5yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

Multiply -8 and 5 to get -40.

$$-40x^{9}y^{6}yz^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

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

$$-40x^{9}y^{7}z^{2}-4x^{9}y^{7}z^{2}\left(-4\right)$$

Multiply 4 and -4 to get -16.

$$-40x^{9}y^{7}z^{2}-\left(-16x^{9}y^{7}z^{2}\right)$$

The opposite of -16x^{9}y^{7}z^{2} is 16x^{9}y^{7}z^{2}.

$$-40x^{9}y^{7}z^{2}+16x^{9}y^{7}z^{2}$$

Combine -40x^{9}y^{7}z^{2} and 16x^{9}y^{7}z^{2} to get -24x^{9}y^{7}z^{2}.

$$-24x^{9}y^{7}z^{2}$$