Solve frac{5d^{8}}{t^{2}}*4t^4/d^3div2d^6/t^5

$$\frac { 5 d ^ { 8 } } { t ^ { 2 } } \times \frac { 4 t ^ { 4 } } { d ^ { 3 } } \div \frac { 2 d ^ { 6 } } { t ^ { 5 } }$$

Evaluate

$$\frac{10t^{7}}{d}$$

Solution Steps

Multiply \frac{5d^{8}}{t^{2}} times \frac{4t^{4}}{d^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5d^{8}\times 4t^{4}}{t^{2}d^{3}}}{\frac{2d^{6}}{t^{5}}}$$

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

$$\frac{4\times 5t^{2}d^{5}}{\frac{2d^{6}}{t^{5}}}$$

Multiply 4 and 5 to get 20.

$$\frac{20t^{2}d^{5}}{\frac{2d^{6}}{t^{5}}}$$

Divide 20t^{2}d^{5} by \frac{2d^{6}}{t^{5}} by multiplying 20t^{2}d^{5} by the reciprocal of \frac{2d^{6}}{t^{5}}.

$$\frac{20t^{2}d^{5}t^{5}}{2d^{6}}$$

Cancel out 2d^{5} in both numerator and denominator.

$$\frac{10t^{2}t^{5}}{d}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{10t^{7}}{d}$$

Differentiate w.r.t. d

$$-\frac{10t^{7}}{d^{2}}$$