Solve (9a^6):(-3a)

$$( 9 a ^ { 6 } ) : ( - 3 a )$$

Evaluate

$$-3a^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}a^{6}}{\left(-3\right)^{1}a^{1}}$$

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

$$\frac{9^{1}a^{6-1}}{\left(-3\right)^{1}}$$

Subtract 1 from 6.

$$\frac{9^{1}a^{5}}{\left(-3\right)^{1}}$$

Divide 9 by -3.

$$-3a^{5}$$

Differentiate w.r.t. a

$$-15a^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{9}{-3}a^{6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-3a^{5})$$

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}.

$$5\left(-3\right)a^{5-1}$$

Do the arithmetic.

$$-15a^{4}$$