Solve (81a^5b):(-9a^4b)

$$( 81 a ^ { 5 } b ) : ( - 9 a ^ { 4 } b )$$

Evaluate

$$-9a$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{81^{1}a^{5}b^{1}}{\left(-9\right)^{1}a^{4}b^{1}}$$

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

$$\frac{81^{1}}{\left(-9\right)^{1}}a^{5-4}b^{1-1}$$

Subtract 4 from 5.

$$\frac{81^{1}}{\left(-9\right)^{1}}a^{1}b^{1-1}$$

Subtract 1 from 1.

$$\frac{81^{1}}{\left(-9\right)^{1}}ab^{0}$$

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

$$\frac{81^{1}}{\left(-9\right)^{1}}a$$

Divide 81 by -9.

$$-9a$$

Differentiate w.r.t. a

$$-9$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{81b}{-9b}a^{5-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-9a^{1})$$

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}.

$$-9a^{1-1}$$

Do the arithmetic.

$$-9a^{0}$$

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

$$-9$$