Solve frac{169^frac{3{3}}b}{134}div120b^2/205^4

$$\frac { 169 ^ { \frac { 3 } { 3 } } b } { 134 } \div \frac { 120 b ^ { 2 } } { 205 ^ { 4 } }$$

Evaluate

$$\frac{59694201125}{3216b}$$

Solution Steps

Divide 3 by 3 to get 1.

$$\frac{\frac{169^{1}b}{134}}{\frac{120b^{2}}{205^{4}}}$$

Divide \frac{169^{1}b}{134} by \frac{120b^{2}}{205^{4}} by multiplying \frac{169^{1}b}{134} by the reciprocal of \frac{120b^{2}}{205^{4}}.

$$\frac{169^{1}b\times 205^{4}}{134\times 120b^{2}}$$

Cancel out b in both numerator and denominator.

$$\frac{169^{1}\times 205^{4}}{120\times 134b}$$

Calculate 169 to the power of 1 and get 169.

$$\frac{169\times 205^{4}}{120\times 134b}$$

Calculate 205 to the power of 4 and get 1766100625.

$$\frac{169\times 1766100625}{120\times 134b}$$

Multiply 169 and 1766100625 to get 298471005625.

$$\frac{298471005625}{120\times 134b}$$

Multiply 120 and 134 to get 16080.

$$\frac{298471005625}{16080b}$$

Differentiate w.r.t. b

$$-\frac{59694201125}{3216b^{2}}$$