Solve 5^3*5^2*t^8/10xt^4

$$\frac { 5 ^ { 3 } \times 5 ^ { 2 } \times t ^ { 8 } } { 10 x t ^ { 4 } }$$

Evaluate

$$\frac{625t^{4}}{2x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{5^{5}t^{8}}{10xt^{4}}$$

Cancel out t^{4} in both numerator and denominator.

$$\frac{5^{5}t^{4}}{10x}$$

Calculate 5 to the power of 5 and get 3125.

$$\frac{3125t^{4}}{10x}$$

Cancel out 5 in both numerator and denominator.

$$\frac{625t^{4}}{2x}$$

Differentiate w.r.t. x

$$-\frac{625t^{4}}{2x^{2}}$$