Solve a^2x/by^2*ay^2/b^2x

$$\frac { a ^ { 2 } x } { b y ^ { 2 } } \cdot \frac { a y ^ { 2 } } { b ^ { 2 } x }$$

Evaluate

$$\left(\frac{a}{b}\right)^{3}$$

Solution Steps

Multiply \frac{a^{2}x}{by^{2}} times \frac{ay^{2}}{b^{2}x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{2}xay^{2}}{by^{2}b^{2}x}$$

Cancel out xy^{2} in both numerator and denominator.

$$\frac{aa^{2}}{bb^{2}}$$

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

$$\frac{a^{3}}{bb^{2}}$$

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

$$\frac{a^{3}}{b^{3}}$$

Differentiate w.r.t. a

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