Hello.
First, let's recall the Properties of Exponents:
[tex]\displaystyle(\frac{a}{b} )^{m}[/tex]= [tex]\displaystyle\frac{a^{m} }{b^{m}}[/tex]
Let's use this property to simplify the given expression:
[tex]\displaystyle(\frac{9}{16} )^\frac{1}{2}[/tex]
[tex]\displaystyle\frac{9^{\frac{1}{2} } }{16\x^{\frac{1}{2} } }[/tex]
Now, the [tex]\frac{1}{2}[/tex] power means "square root of"
The square root of 9 is 3, and the square root of 16 is 4.
Thus, we have
[tex]\displaystyle\frac{\sqrt{9} }{\sqrt{16} } \\\displaystyle\frac{3 }{4}[/tex]
Therefore, the answer is
[tex]\displaystyle\frac{3}{4}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
