Solve (-8x^3y^2z):(-2x^2y^2)=

$$( - 8 x ^ { 3 } y ^ { 2 } z ) : ( - 2 x ^ { 2 } y ^ { 2 } ) =$$

Evaluate

$$4xz$$

Solution Steps

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

$$\frac{-4xz}{-1}$$

Anything divided by -1 gives its opposite.

$$4xz$$

Differentiate w.r.t. x

$$4z$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{8zy^{2}}{-2y^{2}}\right)x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4zx^{1})$$

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}.

$$4zx^{1-1}$$

Do the arithmetic.

$$4zx^{0}$$

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

$$4z\times 1$$

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

$$4z$$