Solve (-8/9a^3bc):(-2a^2bc)=

$$( - \frac { 8 } { 9 } a ^ { 3 } b c ) : ( - 2 a ^ { 2 } b c ) =$$

Evaluate

$$\frac{4a}{9}$$

Solution Steps

Cancel out bca^{2} in both numerator and denominator.

$$\frac{-\frac{8}{9}a}{-2}$$

Divide -\frac{8}{9}a by -2 to get \frac{4}{9}a.

$$\frac{4}{9}a$$

Differentiate w.r.t. a

$$\frac{4}{9} = 0.4444444444444444$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{\frac{8bc}{9}}{-2bc}\right)a^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4}{9}a^{1})$$

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}.

$$\frac{4}{9}a^{1-1}$$

Do the arithmetic.

$$\frac{4}{9}a^{0}$$

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

$$\frac{4}{9}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{4}{9}$$