Solve (-6y^4):y^3=

$$( - 6 y ^ { 4 } ) : y ^ { 3 } =$$

Evaluate

$$-6y$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-6y^{4}\right)^{1}\times \frac{1}{y^{3}}$$

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

$$\left(-6\right)^{1}\left(y^{4}\right)^{1}\times \frac{1}{1}\times \frac{1}{y^{3}}$$

Use the Commutative Property of Multiplication.

$$\left(-6\right)^{1}\times \frac{1}{1}\left(y^{4}\right)^{1}\times \frac{1}{y^{3}}$$

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

$$\left(-6\right)^{1}\times \frac{1}{1}y^{4}y^{3\left(-1\right)}$$

Multiply 3 times -1.

$$\left(-6\right)^{1}\times \frac{1}{1}y^{4}y^{-3}$$

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

$$\left(-6\right)^{1}\times \frac{1}{1}y^{4-3}$$

Add the exponents 4 and -3.

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

Raise -6 to the power 1.

$$-6\times \frac{1}{1}y^{1}$$

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

$$-6\times \frac{1}{1}y$$

Differentiate w.r.t. y

$$-6$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-\frac{6}{1}\right)y^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-6y^{1})$$

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}.

$$-6y^{1-1}$$

Do the arithmetic.

$$-6y^{0}$$

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

$$-6$$