Solve -35a^10b/10a^9b

$$\frac { - 35 a ^ { 10 } b } { 10 a ^ { 9 } b }$$

Evaluate

$$-\frac{7a}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-35\right)^{1}a^{10}b^{1}}{10^{1}a^{9}b^{1}}$$

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

$$\frac{\left(-35\right)^{1}}{10^{1}}a^{10-9}b^{1-1}$$

Subtract 9 from 10.

$$\frac{\left(-35\right)^{1}}{10^{1}}a^{1}b^{1-1}$$

Subtract 1 from 1.

$$\frac{\left(-35\right)^{1}}{10^{1}}ab^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{\left(-35\right)^{1}}{10^{1}}a$$

Reduce the fraction \frac{-35}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{7}{2}a$$

Differentiate w.r.t. a

$$-\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{35b}{10b}\right)a^{10-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{7}{2}a^{1})$$

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}.

$$-\frac{7}{2}a^{1-1}$$

Do the arithmetic.

$$-\frac{7}{2}a^{0}$$

For any term t except 0, t^{0}=1.

$$-\frac{7}{2}$$