# Solve for a sixth root of 1-a^2=0

1-a26=0
To remove the radical on the left side of the equation, raise both sides of the equation to the power of 6.
1-a266=06
Simplify each side of the equation.
Multiply the exponents in ((1-a2)16)6.
Apply the power rule and multiply exponents, (am)n=amn.
(1-a2)16⋅6=06
Cancel the common factor of 6.
Cancel the common factor.
(1-a2)16⋅6=06
Rewrite the expression.
(1-a2)1=06
(1-a2)1=06
(1-a2)1=06
Simplify.
1-a2=06
Raising 0 to any positive power yields 0.
1-a2=0
1-a2=0
Solve for a.
Subtract 1 from both sides of the equation.
-a2=-1
Multiply each term in -a2=-1 by -1
Multiply each term in -a2=-1 by -1.
(-a2)⋅-1=(-1)⋅-1
Multiply (-a2)⋅-1.
Multiply -1 by -1.
1a2=(-1)⋅-1
Multiply a2 by 1.
a2=(-1)⋅-1
a2=(-1)⋅-1
Multiply -1 by -1.
a2=1
a2=1
Take the square root of both sides of the equation to eliminate the exponent on the left side.
a=±1
The complete solution is the result of both the positive and negative portions of the solution.
Any root of 1 is 1.
a=±1
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
a=1
Next, use the negative value of the ± to find the second solution.
a=-1
The complete solution is the result of both the positive and negative portions of the solution.
a=1,-1
a=1,-1
a=1,-1
a=1,-1
Solve for a sixth root of 1-a^2=0

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