Solve 4p^4/4p^-4

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

Evaluate

$$p^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -4 times -1.

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

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

$$4^{1}\times \frac{1}{4}p^{4+4}$$

Add the exponents 4 and 4.

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

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

$$4^{1-1}p^{8}$$

Add the exponents 1 and -1.

$$4^{0}p^{8}$$

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

$$1p^{8}$$

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

$$p^{8}$$

Differentiate w.r.t. p

$$8p^{7}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{8})$$

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}.

$$8p^{8-1}$$

Do the arithmetic.

$$8p^{7}$$