Solve frac{25*6^{2}*2^3}{3^3*a^-4*2^4}

$$\frac { 25 \times 6 ^ { 2 } \times 2 ^ { 3 } } { 3 ^ { 3 } \times a ^ { - 4 } \times 2 ^ { 4 } }$$

Evaluate

$$\frac{50a^{4}}{3}$$

Solution Steps

Cancel out 2^{3} in both numerator and denominator.

$$\frac{25\times 6^{2}}{2\times 3^{3}a^{-4}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{25\times 36}{2\times 3^{3}a^{-4}}$$

Multiply 25 and 36 to get 900.

$$\frac{900}{2\times 3^{3}a^{-4}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{900}{2\times 27a^{-4}}$$

Multiply 2 and 27 to get 54.

$$\frac{900}{54a^{-4}}$$

Differentiate w.r.t. a

$$\frac{200a^{3}}{3}$$