Solve 15x^5z^3:(-3xz^2)

$$15 x ^ { 5 } z ^ { 3 } : ( - 3 x z ^ { 2 } )$$

Evaluate

$$-5zx^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}x^{5}z^{3}}{\left(-3\right)^{1}x^{1}z^{2}}$$

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

$$\frac{15^{1}}{\left(-3\right)^{1}}x^{5-1}z^{3-2}$$

Subtract 1 from 5.

$$\frac{15^{1}}{\left(-3\right)^{1}}x^{4}z^{3-2}$$

Subtract 2 from 3.

$$\frac{15^{1}}{\left(-3\right)^{1}}x^{4}z^{1}$$

Divide 15 by -3.

$$-5x^{4}z$$

Differentiate w.r.t. x

$$-20zx^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15z^{3}}{-3z^{2}}x^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-5z\right)x^{4})$$

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}.

$$4\left(-5z\right)x^{4-1}$$

Do the arithmetic.

$$\left(-20z\right)x^{3}$$