Solve g^-1/g^-9

$$\frac { g ^ { - 1 } } { g ^ { - 9 } }$$

Differentiate w.r.t. g

$$8g^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{1}g^{-1-\left(-9\right)})$$

Do the arithmetic.

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

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}.

$$8g^{8-1}$$

Do the arithmetic.

$$8g^{7}$$

Evaluate

$$g^{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -9 from -1 to get 8.

$$g^{8}$$