Solve frac{3^{3}*(2*3^{5}*5^{2}*a^7b^3}{5^7*(2*3)*a^4b}

$$\frac { 3 ^ { 3 } \times ( 2 \times 3 ^ { 5 } \times 5 ^ { 2 } \times a ^ { 7 } b ^ { 3 } } { 5 ^ { 7 } \times ( 2 \times 3 ) \times a ^ { 4 } b }$$

Evaluate

$$\frac{2187b^{2}a^{3}}{3125}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{3^{8}\times 2\times 5^{2}a^{7}b^{3}}{5^{7}\times 2\times 3a^{4}b}$$

Cancel out 2\times 3\times 5^{2}ba^{4} in both numerator and denominator.

$$\frac{3^{7}b^{2}a^{3}}{5^{5}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{2187b^{2}a^{3}}{5^{5}}$$

Calculate 5 to the power of 5 and get 3125.

$$\frac{2187b^{2}a^{3}}{3125}$$

Differentiate w.r.t. b

$$\frac{4374ba^{3}}{3125}$$