Solve 4^2x^2y^2z^2frac{{4}^{2}{x}^{2}{y}^{2}{z}^{2}}{{2}^2{x}^2{y}^2{z}^2}

$${ 4 }^{ 2 } { x }^{ 2 } { y }^{ 2 } { z }^{ 2 } \frac { { 4 }^{ 2 } { x }^{ 2 } { y }^{ 2 } { z }^{ 2 } } { { 2 }^{ 2 } { x }^{ 2 } { y }^{ 2 } { z }^{ 2 } }$$

Evaluate

$$64\left(xyz\right)^{2}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16x^{2}y^{2}z^{2}\times \frac{4^{2}x^{2}y^{2}z^{2}}{2^{2}x^{2}y^{2}z^{2}}$$

Cancel out x^{2}y^{2}z^{2} in both numerator and denominator.

$$16x^{2}y^{2}z^{2}\times \frac{4^{2}}{2^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}y^{2}z^{2}\times \frac{16}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$16x^{2}y^{2}z^{2}\times \frac{16}{4}$$

Divide 16 by 4 to get 4.

$$16x^{2}y^{2}z^{2}\times 4$$

Multiply 16 and 4 to get 64.

$$64x^{2}y^{2}z^{2}$$

Differentiate w.r.t. x

$$128x\left(yz\right)^{2}$$