Question 886822: i want to know the answer and procedure of this (5^-1)=(x^-6) please solve for x
Answer by GulleyGirlz(1)   (Show Source):
You can put this solution on YOUR website! 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
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