Answer:
1/2 rational exponent represents a square root.
Therefore, option A is correct.
Step-by-step explanation:
As we know that raising to the one-half power i.e. [tex]\frac{1}{2}[/tex] is the same
as taking the square root.
- so [tex]x^{\frac{1}{2}}[/tex] is the same as the square root of [tex]x[/tex].
For example, taking the square root of 4 will determine:
[tex]4^{\frac{1}{2}}[/tex]
[tex]\mathrm{Factor\:the\:number:\:}\:4=2^2[/tex]
[tex]4^{\frac{1}{2}}=\left(2^2\right)^{\frac{1}{2}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0[/tex]
[tex]\left(2^2\right)^{\frac{1}{2}}=2^{2\cdot \frac{1}{2}}[/tex]
so the expression becomes
[tex]4^{\frac{1}{2}}=2^{2\cdot \:\frac{1}{2}}[/tex]
[tex]=2^1[/tex]
[tex]=2[/tex] ∵ [tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a[/tex]
so, 1/2 rational exponent represents a square root.
Therefore, option A is correct.
