Solve 1/3x^{3}y^{2}x(-4x^2y^5)x(-3x)2^3)^2

$$\frac { 1 } { 3 } x ^ { 3 } y ^ { 2 } x ( - 4 x ^ { 2 } y ^ { 5 } ) x ( - 3 x ) 2 ^ { 3 } ) ^ { 2 }$$

Evaluate

$$32y^{7}x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{1}{3}x^{4}y^{2}\left(-4\right)x^{2}y^{5}x\left(-3\right)x\times 2^{3}$$

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

$$\frac{1}{3}x^{6}y^{2}\left(-4\right)y^{5}x\left(-3\right)x\times 2^{3}$$

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

$$\frac{1}{3}x^{7}y^{2}\left(-4\right)y^{5}\left(-3\right)x\times 2^{3}$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{1}{3}x^{8}y^{2}\left(-4\right)y^{5}\left(-3\right)\times 2^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{1}{3}x^{8}y^{7}\left(-4\right)\left(-3\right)\times 2^{3}$$

Multiply \frac{1}{3} and -4 to get -\frac{4}{3}.

$$-\frac{4}{3}x^{8}y^{7}\left(-3\right)\times 2^{3}$$

Multiply -\frac{4}{3} and -3 to get 4.

$$4x^{8}y^{7}\times 2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$4x^{8}y^{7}\times 8$$

Multiply 4 and 8 to get 32.

$$32x^{8}y^{7}$$

Differentiate w.r.t. x

$$256\left(xy\right)^{7}$$