Solve 4^18+y/y=8^14/5*6

$$\frac { 4 ^ { 18 } + y } { y } = \frac { 8 ^ { 14 } } { 5 \cdot 6 }$$

Solve for y

$$y=\frac{1030792151040}{2199023255537}\approx 0.46875$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$4^{18}+y=\frac{1}{30}y\times 8^{14}$$

Calculate 4 to the power of 18 and get 68719476736.

$$68719476736+y=\frac{1}{30}y\times 8^{14}$$

Calculate 8 to the power of 14 and get 4398046511104.

$$68719476736+y=\frac{1}{30}y\times 4398046511104$$

Multiply \frac{1}{30} and 4398046511104 to get \frac{4398046511104}{30}.

$$68719476736+y=\frac{4398046511104}{30}y$$

Reduce the fraction \frac{4398046511104}{30} to lowest terms by extracting and canceling out 2.

$$68719476736+y=\frac{2199023255552}{15}y$$

Subtract \frac{2199023255552}{15}y from both sides.

$$68719476736+y-\frac{2199023255552}{15}y=0$$

Combine y and -\frac{2199023255552}{15}y to get -\frac{2199023255537}{15}y.

$$68719476736-\frac{2199023255537}{15}y=0$$

Subtract 68719476736 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2199023255537}{15}y=-68719476736$$

Multiply both sides by -\frac{15}{2199023255537}, the reciprocal of -\frac{2199023255537}{15}.

$$y=-68719476736\left(-\frac{15}{2199023255537}\right)$$

Express -68719476736\left(-\frac{15}{2199023255537}\right) as a single fraction.

$$y=\frac{-68719476736\left(-15\right)}{2199023255537}$$

Multiply -68719476736 and -15 to get 1030792151040.

$$y=\frac{1030792151040}{2199023255537}$$