Solve 3x/ab^2x/a^2b3/a^3=

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

Evaluate

$$\frac{9x^{2}}{b^{3}a^{6}}$$

Solution Steps

Multiply \frac{3x}{ab^{2}} times \frac{x}{a^{2}b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3xx}{ab^{2}a^{2}b}\times \frac{3}{a^{3}}$$

Multiply \frac{3xx}{ab^{2}a^{2}b} times \frac{3}{a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3xx\times 3}{ab^{2}a^{2}ba^{3}}$$

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

$$\frac{3x^{2}\times 3}{ab^{2}a^{2}ba^{3}}$$

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

$$\frac{3x^{2}\times 3}{a^{3}b^{2}ba^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{3x^{2}\times 3}{a^{6}b^{2}b}$$

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

$$\frac{3x^{2}\times 3}{a^{6}b^{3}}$$

Multiply 3 and 3 to get 9.

$$\frac{9x^{2}}{a^{6}b^{3}}$$

Differentiate w.r.t. x

$$\frac{18x}{b^{3}a^{6}}$$