Question 886822
5−1=x^−6

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. 
x^−6=5^−1

Remove the negative exponent by rewriting 5^−1 as 1/5. A negative exponent follows the rule a^−n=1/a^n.
x^−6=1/5

Remove the negative exponent in the numerator by rewriting x^−6 as 1/x^6. A negative exponent follows the rule: a^−n=1/a^n.
1/x^6=1/5

Set up the rational expression with the same denominator over the entire equation. 
5/5x^6=x^6/5x^6

Since the expression on each side of the equation has the same denominator, the numerators must be equal. 
5=x^6

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. 
x^6=5

Take the +6th root of both sides of the equation to eliminate the exponent on the left-hand side. 
x=±^6√5 

First, substitute in the + portion of the ± to find the first solution. 
x=^6√5

Next, substitute in the − portion of the ± to find the second solution. 
x=−^6√5

The complete solution is the result of both the + and − portions of the solution. 
x=^6√5,−6√5 
x≈1.307660486012,−1.307660486012