Solve frac{a^{2}y^2}{ac^2}div20b^2/a^2bc

$$\frac { a ^ { 2 } y ^ { 2 } } { a c ^ { 2 } } \div \frac { 20 b ^ { 2 } } { a ^ { 2 } b c }$$

Evaluate

$$\frac{y^{2}a^{3}}{20bc}$$

Solution Steps

Divide \frac{a^{2}y^{2}}{ac^{2}} by \frac{20b^{2}}{a^{2}bc} by multiplying \frac{a^{2}y^{2}}{ac^{2}} by the reciprocal of \frac{20b^{2}}{a^{2}bc}.

$$\frac{a^{2}y^{2}a^{2}bc}{ac^{2}\times 20b^{2}}$$

Cancel out abc in both numerator and denominator.

$$\frac{aa^{2}y^{2}}{20bc}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{a^{3}y^{2}}{20bc}$$

Differentiate w.r.t. a

$$\frac{3\left(ay\right)^{2}}{20bc}$$