Solve 4/3a^3b^2:1/9a^2b^2

$$\frac { 4 } { 3 } a ^ { 3 } b ^ { 2 } : \frac { 1 } { 9 } a ^ { 2 } b ^ { 2 }$$

Evaluate

$$12b^{4}a^{5}$$

Solution Steps

Divide \frac{4}{3}a^{3}b^{2} by \frac{1}{9} by multiplying \frac{4}{3}a^{3}b^{2} by the reciprocal of \frac{1}{9}.

$$\frac{4}{3}a^{3}b^{2}\times 9a^{2}b^{2}$$

Multiply \frac{4}{3} and 9 to get 12.

$$12a^{3}b^{2}a^{2}b^{2}$$

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

$$12a^{5}b^{2}b^{2}$$

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

$$12a^{5}b^{4}$$

Differentiate w.r.t. a

$$60\left(ab\right)^{4}$$