Question

Which expression is equivalent to (4^5/4 4^1/4/4^1/2) ^1/2

Answer 1

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

$\rm( {\dfrac{4^{5/4} * 4^{1/4}}{4^{1/2}}})^{1/2}$

By exponent rule

$\rm a^m * a^n = a^{m+n}\\\\a^m \div a^n = a^{m-n}$

Here so ,

$\rm 4^{(\dfrac{5}{4} +\dfrac{1}{4} -\dfrac{1}{2})^{1/2}$

$\rm 4^{(\dfrac{6}{4} -\dfrac{1}{2})^{1/2}$

$4^{(\dfrac{6-2}{4} )^{1/2}$

$4^{1/2}\\\\(2^2)^{1/2}\\\\2$

Therefore the expression is equivalent to 2 , Option C is the correct answer.

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