Solve -7y^8/35y^3

$$\frac { - 7 y ^ { 8 } } { 35 y ^ { 3 } }$$

Evaluate

$$-\frac{y^{5}}{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-7y^{8}\right)^{1}\times \frac{1}{35y^{3}}$$

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

$$\left(-7\right)^{1}\left(y^{8}\right)^{1}\times \frac{1}{35}\times \frac{1}{y^{3}}$$

Use the Commutative Property of Multiplication.

$$\left(-7\right)^{1}\times \frac{1}{35}\left(y^{8}\right)^{1}\times \frac{1}{y^{3}}$$

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

$$\left(-7\right)^{1}\times \frac{1}{35}y^{8}y^{3\left(-1\right)}$$

Multiply 3 times -1.

$$\left(-7\right)^{1}\times \frac{1}{35}y^{8}y^{-3}$$

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

$$\left(-7\right)^{1}\times \frac{1}{35}y^{8-3}$$

Add the exponents 8 and -3.

$$\left(-7\right)^{1}\times \frac{1}{35}y^{5}$$

Raise -7 to the power 1.

$$-7\times \frac{1}{35}y^{5}$$

Multiply -7 times \frac{1}{35}.

$$-\frac{1}{5}y^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-7\right)^{1}y^{8}}{35^{1}y^{3}}$$

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

$$\frac{\left(-7\right)^{1}y^{8-3}}{35^{1}}$$

Subtract 3 from 8.

$$\frac{\left(-7\right)^{1}y^{5}}{35^{1}}$$

Reduce the fraction \frac{-7}{35} to lowest terms by extracting and canceling out 7.

$$-\frac{1}{5}y^{5}$$

Differentiate w.r.t. y

$$-y^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-\frac{7}{35}\right)y^{8-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{5}y^{5})$$

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}.

$$5\left(-\frac{1}{5}\right)y^{5-1}$$

Do the arithmetic.

$$-y^{4}$$