Solve 77a^5b^4/-11ab^4

$$\frac { 77 a ^ { 5 } b ^ { 4 } } { - 11 a b ^ { 4 } }$$

Evaluate

$$-7a^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{77^{1}a^{5}b^{4}}{\left(-11\right)^{1}a^{1}b^{4}}$$

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

$$\frac{77^{1}}{\left(-11\right)^{1}}a^{5-1}b^{4-4}$$

Subtract 1 from 5.

$$\frac{77^{1}}{\left(-11\right)^{1}}a^{4}b^{4-4}$$

Subtract 4 from 4.

$$\frac{77^{1}}{\left(-11\right)^{1}}a^{4}b^{0}$$

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

$$\frac{77^{1}}{\left(-11\right)^{1}}a^{4}$$

Divide 77 by -11.

$$-7a^{4}$$

Differentiate w.r.t. a

$$-28a^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{77b^{4}}{-11b^{4}}a^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-7a^{4})$$

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}.

$$4\left(-7\right)a^{4-1}$$

Do the arithmetic.

$$-28a^{3}$$