42+b2=(69)2

Raise 4 to the power of 2.

16+b2=(69)2

Use axn=axn to rewrite 69 as 6912.

16+b2=(6912)2

Apply the power rule and multiply exponents, (am)n=amn.

16+b2=6912⋅2

Combine 12 and 2.

16+b2=6922

Cancel the common factor of 2.

Cancel the common factor.

16+b2=6922

Divide 1 by 1.

16+b2=691

16+b2=691

Evaluate the exponent.

16+b2=69

16+b2=69

Subtract 16 from both sides of the equation.

b2=69-16

Subtract 16 from 69.

b2=53

b2=53

Take the square root of both sides of the equation to eliminate the exponent on the left side.

b=±53

First, use the positive value of the ± to find the first solution.

b=53

Next, use the negative value of the ± to find the second solution.

b=-53

The complete solution is the result of both the positive and negative portions of the solution.

b=53,-53

b=53,-53

The result can be shown in multiple forms.

Exact Form:

b=53,-53

Decimal Form:

b=7.28010988…,-7.28010988…

Solve for b 4^2+b^2=( square root of 69)^2