Solve frac{5^{8}*a^{5}*10^{3}*2^6}{8*5^9*b^5*2^2}

$$\frac { 5 ^ { 8 } \times a ^ { 5 } \times 10 ^ { 3 } \times 2 ^ { 6 } } { 8 \times 5 ^ { 9 } \times b ^ { 5 } \times 2 ^ { 2 } }$$

Evaluate

$$400\times \left(\frac{a}{b}\right)^{5}$$

Solution Steps

Cancel out 2^{2}\times 5^{8} in both numerator and denominator.

$$\frac{2^{4}\times 10^{3}a^{5}}{5\times 8b^{5}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16\times 10^{3}a^{5}}{5\times 8b^{5}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{16\times 1000a^{5}}{5\times 8b^{5}}$$

Multiply 16 and 1000 to get 16000.

$$\frac{16000a^{5}}{5\times 8b^{5}}$$

Multiply 5 and 8 to get 40.

$$\frac{16000a^{5}}{40b^{5}}$$

Cancel out 40 in both numerator and denominator.

$$\frac{400a^{5}}{b^{5}}$$

Differentiate w.r.t. a

$$\frac{2000a^{4}}{b^{5}}$$