Solve f(-8)^-5*(-8)^-4]:(-8)^-11

$$f ( - 8 ) ^ { - 5 } \cdot ( - 8 ) ^ { - 4 } ] : ( - 8 ) ^ { - 11 }$$

Evaluate

$$-\frac{f}{134217728}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and -4 to get -9.

$$f\left(-8\right)^{-9}$$

Calculate -8 to the power of -9 and get -\frac{1}{134217728}.

$$f\left(-\frac{1}{134217728}\right)$$

Differentiate w.r.t. f

$$-\frac{1}{134217728} = -7.450580596923827 \times 10^{-9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and -4 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\left(-8\right)^{-9})$$

Calculate -8 to the power of -9 and get -\frac{1}{134217728}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\left(-\frac{1}{134217728}\right))$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{1}{134217728}f^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{134217728}f^{0}$$

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

$$-\frac{1}{134217728}$$