Solve 5x/9x^3div15x/25x^0

$$\frac { 5 x } { 9 x ^ { 3 } } \div \frac { 15 x } { 25 x ^ { 0 } }$$

Evaluate

$$\frac{25}{27x^{3}}$$

Solution Steps

Divide \frac{5x}{9x^{3}} by \frac{15x}{25x^{0}} by multiplying \frac{5x}{9x^{3}} by the reciprocal of \frac{15x}{25x^{0}}.

$$\frac{5x\times 25x^{0}}{9x^{3}\times 15x}$$

Cancel out 5x in both numerator and denominator.

$$\frac{25x^{0}}{3\times 9xx^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{25}{3\times 9xx^{2}}$$

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

$$\frac{25}{3\times 9x^{3}}$$

Multiply 3 and 9 to get 27.

$$\frac{25}{27x^{3}}$$

Differentiate w.r.t. x

$$-\frac{25}{9x^{4}}$$