Simplify \(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)
Question 1 Report
Simplify \(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)
Answer Details
We can simplify this expression using the rules of exponents and radicals.
First, we can rewrite 9 as \(3^2\) and 27 as \(3^3\):
\(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}} = \frac{(3^2)^{-\frac{1}{2}}}{(3^3)^{\frac{2}{3}}}\)
Next, we can simplify the exponents using the product rule of exponents:
\(\frac{(3^2)^{-\frac{1}{2}}}{(3^3)^{\frac{2}{3}}} = \frac{3^{-1}}{3^2} = \frac{1}{3^{1+2}} = \frac{1}{3^3} = \frac{1}{27}\)
Therefore, the simplified expression is 1/27.
The answer is option E.
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