Compare (1/2)⁵ and (0.5)⁵: Exploring Exponential Equivalence

To solve this problem, we'll follow these steps:

• Step 1: Recognize that $\frac{1}{2}$ is equivalent to $0.5$.

• Step 2: Evaluate both expressions using this equivalence.

• Step 3: Conclude based on the equality of the expressions.

Now, let's work through each step:
Step 1: It's important to understand the equivalence between $\frac{1}{2}$ and $0.5$. As a fraction, $\frac{1}{2}$ is equal to the decimal $0.5$.
Step 2: We apply the power to each base: $(\frac{1}{2})^5$ and $(0.5)^5$. Due to their equivalence, $(\frac{1}{2})^5$ is necessarily equal to $(0.5)^5$.
Step 3: Since both expressions compute to the same value because their bases are identical ($\frac{1}{2} = 0.5$), the two expressions are equal.

Therefore, the solution to the problem is$=$.