Solve 6p^-2/p^2

$$\frac { 6 p ^ { - 2 } } { p ^ { 2 } }$$

Evaluate

$$\frac{6}{p^{4}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6p^{-2}\right)^{1}\times \frac{1}{p^{2}}$$

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

$$6^{1}\left(p^{-2}\right)^{1}\times \frac{1}{1}\times \frac{1}{p^{2}}$$

Use the Commutative Property of Multiplication.

$$6^{1}\times \frac{1}{1}\left(p^{-2}\right)^{1}\times \frac{1}{p^{2}}$$

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

$$6^{1}\times \frac{1}{1}p^{-2}p^{2\left(-1\right)}$$

Multiply 2 times -1.

$$6^{1}\times \frac{1}{1}p^{-2}p^{-2}$$

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

$$6^{1}\times \frac{1}{1}p^{-2-2}$$

Add the exponents -2 and -2.

$$6^{1}\times \frac{1}{1}p^{-4}$$

Raise 6 to the power 1.

$$6\times \frac{1}{1}p^{-4}$$

Differentiate w.r.t. p

$$-\frac{24}{p^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{6}{1}p^{-2-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(6p^{-4})$$

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}.

$$-4\times 6p^{-4-1}$$

Do the arithmetic.

$$-24p^{-5}$$