Solve -8p^8/8p^4

$$\frac { - 8 p ^ { 8 } } { 8 p ^ { 4 } }$$

Evaluate

$$-p^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-8p^{8}\right)^{1}\times \frac{1}{8p^{4}}$$

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

$$\left(-8\right)^{1}\left(p^{8}\right)^{1}\times \frac{1}{8}\times \frac{1}{p^{4}}$$

Use the Commutative Property of Multiplication.

$$\left(-8\right)^{1}\times \frac{1}{8}\left(p^{8}\right)^{1}\times \frac{1}{p^{4}}$$

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

$$\left(-8\right)^{1}\times \frac{1}{8}p^{8}p^{4\left(-1\right)}$$

Multiply 4 times -1.

$$\left(-8\right)^{1}\times \frac{1}{8}p^{8}p^{-4}$$

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

$$\left(-8\right)^{1}\times \frac{1}{8}p^{8-4}$$

Add the exponents 8 and -4.

$$\left(-8\right)^{1}\times \frac{1}{8}p^{4}$$

Raise -8 to the power 1.

$$-8\times \frac{1}{8}p^{4}$$

Multiply -8 times \frac{1}{8}.

$$-p^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-8\right)^{1}p^{8}}{8^{1}p^{4}}$$

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

$$\frac{\left(-8\right)^{1}p^{8-4}}{8^{1}}$$

Subtract 4 from 8.

$$\frac{\left(-8\right)^{1}p^{4}}{8^{1}}$$

Divide -8 by 8.

$$-p^{4}$$

Differentiate w.r.t. p

$$-4p^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\left(-\frac{8}{8}\right)p^{8-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-p^{4})$$

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}.

$$4\left(-1\right)p^{4-1}$$

Do the arithmetic.

$$-4p^{3}$$