Solve -15x^3y^2:(-3/5x^2y^2)=

$$- 15 x ^ { 3 } y ^ { 2 } : ( - \frac { 3 } { 5 } x ^ { 2 } y ^ { 2 } ) =$$

Evaluate

$$25x$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 3.

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

Subtract 2 from 2.

$$\frac{\left(-15\right)^{1}}{\left(-\frac{3}{5}\right)^{1}}xy^{0}$$

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

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

Divide -15 by -\frac{3}{5} by multiplying -15 by the reciprocal of -\frac{3}{5}.

$$25x$$

Differentiate w.r.t. x

$$25$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{15y^{2}}{-\frac{3y^{2}}{5}}\right)x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{1})$$

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}.

$$25x^{1-1}$$

Do the arithmetic.

$$25x^{0}$$

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

$$25\times 1$$

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

$$25$$