Solve 70y^2left(2^2right)^/frac{5{2}}yz

$$\frac{ 70 { y }^{ 2 } { \left( { 2 }^{ 2 } \right) }^{ } }{ \frac{ 5 }{ 2 } } yz$$

Evaluate

$$112zy^{3}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 1 to get 2.

$$\frac{70y^{2}\times 2^{2}}{\frac{5}{2}}yz$$

Calculate 2 to the power of 2 and get 4.

$$\frac{70y^{2}\times 4}{\frac{5}{2}}yz$$

Multiply 70 and 4 to get 280.

$$\frac{280y^{2}}{\frac{5}{2}}yz$$

Divide 280y^{2} by \frac{5}{2} by multiplying 280y^{2} by the reciprocal of \frac{5}{2}.

$$\frac{280y^{2}\times 2}{5}yz$$

Multiply 280 and 2 to get 560.

$$\frac{560y^{2}}{5}yz$$

Divide 560y^{2} by 5 to get 112y^{2}.

$$112y^{2}yz$$

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

$$112y^{3}z$$

Differentiate w.r.t. z

$$112y^{3}$$