Solve 7p^5/p^-1

$$\frac { 7 p ^ { 5 } } { p ^ { - 1 } }$$

Evaluate

$$7p^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(7p^{5}\right)^{1}\times \frac{1}{\frac{1}{p}}$$

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

$$7^{1}\left(p^{5}\right)^{1}\times \frac{1}{1}\times \frac{1}{\frac{1}{p}}$$

Use the Commutative Property of Multiplication.

$$7^{1}\times \frac{1}{1}\left(p^{5}\right)^{1}\times \frac{1}{\frac{1}{p}}$$

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

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

Multiply -1 times -1.

$$7^{1}\times \frac{1}{1}p^{5}p^{1}$$

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

$$7^{1}\times \frac{1}{1}p^{5+1}$$

Add the exponents 5 and 1.

$$7^{1}\times \frac{1}{1}p^{6}$$

Raise 7 to the power 1.

$$7\times \frac{1}{1}p^{6}$$

Differentiate w.r.t. p

$$42p^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{7}{1}p^{5-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(7p^{6})$$

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}.

$$6\times 7p^{6-1}$$

Do the arithmetic.

$$42p^{5}$$