this module is intended to help you understand fractional exponents. rewrite the expression below as 4 to a…

this module is intended to help you understand fractional exponents. rewrite the expression below as 4 to a single power: \n$(4^2)^{10}=4^{20}$\n$(4^6)^3=4^{18}$\nnow try:\n$(4^{\frac{1}{2}})^2=\\boxed{}$

this module is intended to help you understand fractional exponents. rewrite the expression below as 4 to a single power: \n$(4^2)^{10}=4^{20}$\n$(4^6)^3=4^{18}$\nnow try:\n$(4^{\frac{1}{2}})^2=\\boxed{}$

Answer

Explanation:

Step1: Recall the power - of - a - power rule

The power - of - a - power rule states that ((a^{m})^{n}=a^{m\times n}), where (a) is the base and (m) and (n) are exponents. In the given expression (\left(4^{\frac{1}{2}}\right)^{2}), the base (a = 4), (m=\frac{1}{2}) and (n = 2).

Step2: Apply the power - of - a - power rule

Using the formula ((a^{m})^{n}=a^{m\times n}), we substitute (a = 4), (m=\frac{1}{2}) and (n = 2) into the formula. So we have (4^{\frac{1}{2}\times2}).

Step3: Simplify the exponent

Simplify (\frac{1}{2}\times2). (\frac{1}{2}\times2 = 1). So the expression becomes (4^{1}).

Step4: Evaluate (4^{1})

Any non - zero number raised to the power of 1 is the number itself. So (4^{1}=4).

Answer:

(4)