Solve p^-3divp^-4

$$p ^ { - 3 } \div p ^ { - 4 }$$

Evaluate

$$p$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from -3 to get 1.

$$p^{1}$$

Calculate p to the power of 1 and get p.

$$p$$

Differentiate w.r.t. p

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{1}p^{-3-\left(-4\right)})$$

Do the arithmetic.

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

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}.

$$p^{1-1}$$

Do the arithmetic.

$$p^{0}$$

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

$$1$$