Solve F=(16^{-4}-1)^{-1}+(25^-2-1)^-1+(64^-3-1)^-1

$$F = ( 16 ^ { - 4 } - 1 ) ^ { - 1 } + ( 25 ^ { - 2 } - 1 ) ^ { - 1 } + ( 64 ^ { - 3 - 1 } ) ^ { - 1 }$$

Solve for F

$$F = \frac{76231633877289}{4543760} = 16777213\frac{4536409}{4543760} \approx 16777213.998382177$$

Steps for Solving Linear Equation

Calculate 16 to the power of -4 and get \frac{1}{65536}.

$$F=\left(\frac{1}{65536}-1\right)^{-1}+\left(25^{-2}-1\right)^{-1}+\left(64^{-3-1}\right)^{-1}$$

Subtract 1 from \frac{1}{65536} to get -\frac{65535}{65536}.

$$F=\left(-\frac{65535}{65536}\right)^{-1}+\left(25^{-2}-1\right)^{-1}+\left(64^{-3-1}\right)^{-1}$$

Calculate -\frac{65535}{65536} to the power of -1 and get -\frac{65536}{65535}.

$$F=-\frac{65536}{65535}+\left(25^{-2}-1\right)^{-1}+\left(64^{-3-1}\right)^{-1}$$

Calculate 25 to the power of -2 and get \frac{1}{625}.

$$F=-\frac{65536}{65535}+\left(\frac{1}{625}-1\right)^{-1}+\left(64^{-3-1}\right)^{-1}$$

Subtract 1 from \frac{1}{625} to get -\frac{624}{625}.

$$F=-\frac{65536}{65535}+\left(-\frac{624}{625}\right)^{-1}+\left(64^{-3-1}\right)^{-1}$$

Calculate -\frac{624}{625} to the power of -1 and get -\frac{625}{624}.

$$F=-\frac{65536}{65535}-\frac{625}{624}+\left(64^{-3-1}\right)^{-1}$$

Subtract \frac{625}{624} from -\frac{65536}{65535} to get -\frac{9094871}{4543760}.

$$F=-\frac{9094871}{4543760}+\left(64^{-3-1}\right)^{-1}$$

Subtract 1 from -3 to get -4.

$$F=-\frac{9094871}{4543760}+\left(64^{-4}\right)^{-1}$$

Calculate 64 to the power of -4 and get \frac{1}{16777216}.

$$F=-\frac{9094871}{4543760}+\left(\frac{1}{16777216}\right)^{-1}$$

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

$$F=-\frac{9094871}{4543760}[phone]$$

Add -\frac{9094871}{4543760} and 16777216 to get \frac{76231633877289}{4543760}.

$$F=\frac{76231633877289}{4543760}$$

Assign F

$$F≔\frac{76231633877289}{4543760}$$