Answer: [tex](\sqrt{16})^2= 16[/tex]
[tex]16^{\frac{1}{2}}[/tex] must equal [tex]\sqrt{16}[/tex] in radical form.
Step-by-step explanation: Given radical expression [tex](\sqrt{16})^2[/tex].
First we would convert square root by exponent form.
Square root represents power 1/2.
Therefore,
[tex](\sqrt{16})^2= (16^{1/2})^2[/tex]
We know power rule [tex](x^a)^b= x^{a\times b}[/tex].
Therefore,
By the Power of Power rule,
[tex](16^{1/2})^2 = 16^{1/2 \times 2}[/tex]
On simplifying powers, we get [tex]1/2 \times 2 = 1[/tex].
Therefore, [tex]16^{1/2 \times 2} = 16.[/tex].
So, [tex]16^{\frac{1}{2}}[/tex] must equal [tex]\sqrt{16}[/tex] in radical form.
