Question

Which expression is equivalent to (F)
(1/√y) -1/5

1/√y5

10√y

5 √y2

1/10y

Answer 1

To simplify the expression \( \left( \frac{1}{\sqrt{y}} \right) - \frac{1}{5} \) and determine which expression it matches, let's analyze it step by step.

1. The term \( \frac{1}{\sqrt{y}} \) can be expressed as \( y^{-1/2} \).
2. Thus, the entire expression becomes:
\[
y^{-1/2} - \frac{1}{5}
\]

This expression simplifies to:
\[
\frac{1}{\sqrt{y}} - \frac{1}{5}
\]

Now, we will analyze the provided options:

1. \( \frac{1}{\sqrt{y^5}} \) can be written as \( \frac{1}{y^{5/2}} \), which is not equivalent.

2. \( 10\sqrt{y} \), is not relevant since it represents multiplication and addition of terms that are not comparable.

3. \( 5\sqrt{y^2} \) simplifies to \( 5y \), which is not equivalent.

4. \( \frac{1}{10y} \) simplifies to \( 0.1y^{-1} \), which is not equivalent.

None of the provided expressions are equivalent to \( \left( \frac{1}{\sqrt{y}} \right) - \frac{1}{5} \).

Thus, we should clarify if there's a possible simplification mistake or to ensure impartial representations, please check to confirm the context of \( (F) \) and refactor the original expression based on detailed aspects we observe. If \( \left( \frac{1}{\sqrt{y}} - \frac{1}{5} \) will amass into different equivalent forms, kindly specify if further rewiring through multiplication or standard comparisons may exist.

In conclusion, within the context, none of the provided options are equivalent to your original expression \( \left( \frac{1}{\sqrt{y}} \right) - \frac{1}{5} \).