To remove the negative exponent, move the (6x)^(-(1)/(2)) to the denominator and make the exponent positive.
(1)/((6x)^((1)/(2)))
Expand the exponent ((1)/(2)) to the expression.
(1)/(6^((1)/(2))x^((1)/(2)))
An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent.
(1)/(~((6)))
Remove the parentheses around the expression 6.
(1)/(~(6))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is (~(6))/(~(6)).
(1)/(~(6))*(~(6))/(~(6))
To eliminate the radical from the denominator, multiply ~(6) by ~(6) to get 6.
(~(6))/(6)
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~((1)/(6)*x)
Multiply 1 by x to get x.
~((x)/(6))
Split the fraction inside the radical into a separate radical expression in the numerator and the denominator. A fraction of roots is equivalent to a root of the fraction.
(~(x))/(~(6))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is (~(6))/(~(6)).
(~(x))/(~(6))*(~(6))/(~(6))
Multiply the original expression by a factor of 1 ((~(6))/(~(6))) to eliminate the radical from the denominator.
Answers & Comments
Verified answer
Dear User,
(6x)^(-(1)/(2))
To remove the negative exponent, move the (6x)^(-(1)/(2)) to the denominator and make the exponent positive.
(1)/((6x)^((1)/(2)))
Expand the exponent ((1)/(2)) to the expression.
(1)/(6^((1)/(2))x^((1)/(2)))
An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent.
(1)/(~((6)))
Remove the parentheses around the expression 6.
(1)/(~(6))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is (~(6))/(~(6)).
(1)/(~(6))*(~(6))/(~(6))
To eliminate the radical from the denominator, multiply ~(6) by ~(6) to get 6.
(~(6))/(6)
===============
~((1)/(6)*x)
Multiply 1 by x to get x.
~((x)/(6))
Split the fraction inside the radical into a separate radical expression in the numerator and the denominator. A fraction of roots is equivalent to a root of the fraction.
(~(x))/(~(6))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is (~(6))/(~(6)).
(~(x))/(~(6))*(~(6))/(~(6))
Multiply the original expression by a factor of 1 ((~(6))/(~(6))) to eliminate the radical from the denominator.
(~(x)*~(6))/(6)
Multiply (x) by (6) to get (x)(6).
(~((x)(6)))/(6)
Remove the parentheses.
(~(x(6)))/(6)
Remove the parentheses.
(~(x*6))/(6)
Multiply x by 6 to get 6x.
(~((6x)))/(6)
Remove the parentheses.
(~(6x))/(6)
YES.