Solve 150a^3b^4/20a^2bdiv6b/8ab^2

$$\frac { 150 a ^ { 3 } b ^ { 4 } } { 20 a ^ { 2 } b } \div \frac { 6 b } { 8 a b ^ { 2 } }$$

Evaluate

$$10a^{2}b^{4}$$

Solution Steps

Divide \frac{150a^{3}b^{4}}{20a^{2}b} by \frac{6b}{8ab^{2}} by multiplying \frac{150a^{3}b^{4}}{20a^{2}b} by the reciprocal of \frac{6b}{8ab^{2}}.

$$\frac{150a^{3}b^{4}\times 8ab^{2}}{20a^{2}b\times 6b}$$

Cancel out 2\times 2\times 3\times 10bba^{2} in both numerator and denominator.

$$2\times 5aab^{2}b^{2}$$

Multiply 2 and 5 to get 10.

$$10aab^{2}b^{2}$$

Multiply a and a to get a^{2}.

$$10a^{2}b^{2}b^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$10a^{2}b^{4}$$

Differentiate w.r.t. a

$$20ab^{4}$$