Solve -18y^6div(-9y^3)

$$-18 { y }^{ 6 } \div (-9 { y }^{ 3 } )$$

Evaluate

$$2y^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-18y^{6}\right)^{1}\times \frac{1}{-9y^{3}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-18\right)^{1}\left(y^{6}\right)^{1}\times \frac{1}{-9}\times \frac{1}{y^{3}}$$

Use the Commutative Property of Multiplication.

$$\left(-18\right)^{1}\times \frac{1}{-9}\left(y^{6}\right)^{1}\times \frac{1}{y^{3}}$$

To raise a power to another power, multiply the exponents.

$$\left(-18\right)^{1}\times \frac{1}{-9}y^{6}y^{3\left(-1\right)}$$

Multiply 3 times -1.

$$\left(-18\right)^{1}\times \frac{1}{-9}y^{6}y^{-3}$$

To multiply powers of the same base, add their exponents.

$$\left(-18\right)^{1}\times \frac{1}{-9}y^{6-3}$$

Add the exponents 6 and -3.

$$\left(-18\right)^{1}\times \frac{1}{-9}y^{3}$$

Raise -18 to the power 1.

$$-18\times \frac{1}{-9}y^{3}$$

Raise -9 to the power -1.

$$-18\left(-\frac{1}{9}\right)y^{3}$$

Multiply -18 times -\frac{1}{9}.

$$2y^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-18\right)^{1}y^{6}}{\left(-9\right)^{1}y^{3}}$$

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

$$\frac{\left(-18\right)^{1}y^{6-3}}{\left(-9\right)^{1}}$$

Subtract 3 from 6.

$$\frac{\left(-18\right)^{1}y^{3}}{\left(-9\right)^{1}}$$

Divide -18 by -9.

$$2y^{3}$$

Differentiate w.r.t. y

$$6y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-\frac{18}{-9}\right)y^{6-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{3})$$

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}.

$$3\times 2y^{3-1}$$

Do the arithmetic.

$$6y^{2}$$