The simplified form of the expression [tex]\frac{1}{x^{\frac{-3}{6}}}[/tex] is [tex]\boxed{\sqrt{x}}[/tex].
Further explanation:
The negative exponent in the expression can be removed by the reciprocal of the term in the expression.
The above statement is the property of the exponent. It can be mathematically expressed as follows:
[tex]\boxed{\dfrac{1}{x^{-n}}=x^{n}}[/tex]
In the expression [tex]\sqrt[\frac{1}{n}]{x}[/tex] , [tex]x[/tex] is the radicand, [tex]\frac{1}{n}[/tex] is the radical and [tex]n[/tex] belongs to natural number.
The steps are involved to convert the fraction in the lowest form as,
1) First break the denominator and numerator into their prime factors.
2) Then cut the common factors from numerators and denominators.
3) The resultant fraction would be the lowest form of the given fraction.
Given:
The given expression is [tex]\dfrac{1}{x^{\frac{-3}{6}}}[/tex].
Step 1:
First we remove the negative exponent from the given expression [tex]\dfrac{1}{x^{\frac{-3}{6}}}[/tex].
Use the property of the exponent to remove the negative exponent in the expression.
[tex]\boxed{\dfrac{1}{x^{\frac{-3}{6}}}=x^{\frac{3}{6}}}[/tex]
Step 2:
Now, reduce the exponent of the expression in the lowest form.
[tex]\boxed{x^{\dfrac{3}{6}}=x^{\dfrac{1}{2}}}[/tex]
The above expression [tex]x^{\frac{1}{2}}[/tex] can be written as [tex]\sqrt{x}[/tex].
In the expression [tex]\sqrt{x}[/tex], [tex]x[/tex] is the radicand and [tex]\frac{1}{2}[/tex] is the radical.
Therefore, the simplified form of the expression [tex]\dfrac{1}{x^{\frac{-3}{6}}}[/tex] is [tex]\boxed{\sqrt{x}}[/tex].
Learn more:
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Simplification
Keywords: Radical, exponent, radicand, expressions, variable, factors, lowest form, simplified form, denominators, numerators, property of the exponent, negative exponent, natural number.
