The expression is equivalent to 2 , Option C is the correct answer.
What is an Expression ?
An expression is a mathematical statement consisting of variables , constants and mathematical operators.
The expression given in the question is
[tex]\rm( {\dfrac{4^{5/4} * 4^{1/4}}{4^{1/2}}})^{1/2}[/tex]
By exponent rule
[tex]\rm a^m * a^n = a^{m+n}\\\\a^m \div a^n = a^{m-n}[/tex]
Here so ,
[tex]\rm 4^{(\dfrac{5}{4} +\dfrac{1}{4} -\dfrac{1}{2})^{1/2}[/tex]
[tex]\rm 4^{(\dfrac{6}{4} -\dfrac{1}{2})^{1/2}\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\[/tex]
[tex]4^{(\dfrac{6-2}{4} )^{1/2}\\[/tex]
[tex]4^{1/2}\\\\(2^2)^{1/2}\\\\2[/tex]
Therefore the expression is equivalent to 2 , Option C is the correct answer.
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