Solve F:8^8*(-1/4)^12=

$$F : 8 ^ { 8 } \times ( - \frac { 1 } { 4 } ) ^ { 12 } =$$

Evaluate

$$\frac{F}{281474976710656}$$

Solution Steps

Calculate 8 to the power of 8 and get 16777216.

$$\frac{F}{16777216}\left(-\frac{1}{4}\right)^{12}$$

Calculate -\frac{1}{4} to the power of 12 and get \frac{1}{16777216}.

$$\frac{F}{16777216}\times \frac{1}{16777216}$$

Multiply \frac{F}{16777216} times \frac{1}{16777216} by multiplying numerator times numerator and denominator times denominator.

$$\frac{F}{16777216\times 16777216}$$

Multiply 16777216 and 16777216 to get 281474976710656.

$$\frac{F}{281474976710656}$$

Differentiate w.r.t. F

$$\frac{1}{281474976710656} = 3.5527136788005005 \times 10^{-15}$$

Steps Using Definition of a Derivative

Calculate 8 to the power of 8 and get 16777216.

$$\frac{\mathrm{d}}{\mathrm{d}F}(\frac{F}{16777216}\left(-\frac{1}{4}\right)^{12})$$

Calculate -\frac{1}{4} to the power of 12 and get \frac{1}{16777216}.

$$\frac{\mathrm{d}}{\mathrm{d}F}(\frac{F}{16777216}\times \frac{1}{16777216})$$

Multiply \frac{F}{16777216} times \frac{1}{16777216} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}F}(\frac{F}{16777216\times 16777216})$$

Multiply 16777216 and 16777216 to get 281474976710656.

$$\frac{\mathrm{d}}{\mathrm{d}F}(\frac{F}{281474976710656})$$

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

$$\frac{1}{281474976710656}F^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{281474976710656}F^{0}$$

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

$$\frac{1}{281474976710656}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{281474976710656}$$