Solve 25x^4b^2/15x^2b

$$\frac { 25 x ^ { 4 } b ^ { 2 } } { 15 x ^ { 2 } b }$$

Evaluate

$$\frac{5bx^{2}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{25^{1}x^{4}b^{2}}{15^{1}x^{2}b^{1}}$$

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

$$\frac{25^{1}}{15^{1}}x^{4-2}b^{2-1}$$

Subtract 2 from 4.

$$\frac{25^{1}}{15^{1}}x^{2}b^{2-1}$$

Subtract 1 from 2.

$$\frac{25^{1}}{15^{1}}x^{2}b^{1}$$

Reduce the fraction \frac{25}{15} to lowest terms by extracting and canceling out 5.

$$\frac{5}{3}x^{2}b$$

Differentiate w.r.t. x

$$\frac{10bx}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{25b^{2}}{15b}x^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5b}{3}x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{5b}{3}x^{2-1}$$

Do the arithmetic.

$$\frac{10b}{3}x^{1}$$

For any term t, t^{1}=t.

$$\frac{10b}{3}x$$