Solve 6x^4y^2*4/9xyz*3/4xz^2

$$6 { x }^{ 4 } { y }^{ 2 } \times \frac{ 4 }{ 9 } xyz \times \frac{ 3 }{ 4 } x { z }^{ 2 }$$

Evaluate

$$2x^{6}\left(yz\right)^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$6x^{5}y^{2}\times \frac{4}{9}yz\times \frac{3}{4}xz^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$6x^{6}y^{2}\times \frac{4}{9}yz\times \frac{3}{4}z^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$6x^{6}y^{3}\times \frac{4}{9}z\times \frac{3}{4}z^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$6x^{6}y^{3}\times \frac{4}{9}z^{3}\times \frac{3}{4}$$

Multiply 6 and \frac{4}{9} to get \frac{8}{3}.

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

Multiply \frac{8}{3} and \frac{3}{4} to get 2.

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

Differentiate w.r.t. x

$$12x^{5}\left(yz\right)^{3}$$