(1.68)32=(1+r4)32

Rewrite the equation as (1+r4)32=(1.68)32.

(1+r4)32=(1.68)32

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

|1+r4|=|1.68|

The absolute value is the distance between a number and zero. The distance between 0 and 1.68 is 1.68.

|1+r4|=1.68

Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.

1+r4=±1.68

Set up the positive portion of the ± solution.

1+r4=1.68

Solve the first equation for r.

Move all terms not containing r to the right side of the equation.

Subtract 1 from both sides of the equation.

r4=1.68-1

Subtract 1 from 1.68.

r4=0.68

r4=0.68

Multiply both sides of the equation by 4.

4⋅r4=4⋅0.68

Simplify both sides of the equation.

Cancel the common factor of 4.

Cancel the common factor.

4⋅r4=4⋅0.68

Rewrite the expression.

r=4⋅0.68

r=4⋅0.68

Multiply 4 by 0.68.

r=2.72

r=2.72

r=2.72

Set up the negative portion of the ± solution.

1+r4=-1.68

Solve the second equation for r.

Move all terms not containing r to the right side of the equation.

Subtract 1 from both sides of the equation.

r4=-1.68-1

Subtract 1 from -1.68.

r4=-2.68

r4=-2.68

Multiply both sides of the equation by 4.

4⋅r4=4⋅-2.68

Simplify both sides of the equation.

Cancel the common factor of 4.

Cancel the common factor.

4⋅r4=4⋅-2.68

Rewrite the expression.

r=4⋅-2.68

r=4⋅-2.68

Multiply 4 by -2.68.

r=-10.72

r=-10.72

r=-10.72

The solution to the equation includes both the positive and negative portions of the solution.

r=2.72,-10.72

r=2.72,-10.72

Solve for r (1.68)^32=(1+r/4)^32