For each value of y, determine whether it is a solution to =9÷y4.y Is it a solution?Yes No32 28 44 48

To determine if each value of $y$ is a solution to the equation $9 \div y^4 = y$, we can follow these steps:

1. Break Down the Problem

We need to evaluate the expression $9 \div y^4$ and check if it equals $y$ for each provided value of $y$.

2. Relevant Concepts

The equation can be rewritten as: $\frac{9}{y^4} = y$ Multiplying both sides by $y^4$ gives us: $9 = y^5$ We can find $y$ by taking the fifth root of 9: $y = 9^{1/5}$

3. Analysis and Detail

Now, we will evaluate for each value:

• For $y = 32$: $32^5$ Clearly $32^5$ is much greater than 9, thus $y=32$ is not a solution.

• For $y = 28$: $28^5$ Similar to $32$, $28^5$ is also significantly greater than 9, hence $y=28$ is not a solution.

• For $y = 44$: $44^5$ Again, $44^5$ is also greater than 9, therefore $y=44$ is not a solution.

• For $y = 48$: $48^5$ Likewise, $48^5$ is much larger than 9, so $y=48$ is not a solution.

4. Verify and Summarize

After evaluating each candidate, none of the provided values $32$, $28$, $44$, or $48$ satisfy the equation $9 = y^5$.

Final Answer

None of the values $32$, $28$, $44$, or $48$ are solutions. Hence:

• Is it a solution? No for all values.