What is x^{1/2}((1+1)/x)^{1/2} ?

The solution to x^{1/2}((1+1)/x)^{1/2} is x^{1/2}(2/x)^{1/2}

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simplify x^{1/2}((1+1)/x)^{1/2}

simplify

x^{\frac{1}{2}} (\frac{1 + 1}{x})^{\frac{1}{2}}

x^{\frac{1}{2}} (\frac{2}{x})^{\frac{1}{2}}

Solution steps

x^{\frac{1}{2}} (\frac{1 + 1}{x})^{\frac{1}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1 + 1}{x})^{\frac{1}{2}} = \frac{( 1 + 1 ) ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

= x^{\frac{1}{2}} \frac{( 1 + 1 ) ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

Add the numbers:

1 + 1 = 2

= x^{\frac{1}{2}} \frac{2 ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

Combine same powers :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = (\frac{x ^{a}}{y ^{b}})^{\frac{1}{m}}

= x^{\frac{1}{2}} (\frac{2}{x})^{\frac{1}{2}}

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What is x^{1/2}((1+1)/x)^{1/2} ?
The solution to x^{1/2}((1+1)/x)^{1/2} is x^{1/2}(2/x)^{1/2}