Insert the corresponding expression:
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Insert the corresponding expression:
To solve this problem, let's follow these steps:
Now, let's proceed through each step in detail:
Step 1: We start with the given expression .
Step 2: According to the rule for powers of fractions, we write this expression as:
.
Step 3: This simplification converts both the numerator and the denominator's power into a single power of the fraction .
Therefore, the expression is equivalent to .
Comparing with the given answer choices, the correct choice is \( \text{Choice 2: } .
\( \)Choose the corresponding expression:
\( \left(\frac{1}{2}\right)^2= \)
The quotient rule for exponents tells us that when you have the same exponent on both numerator and denominator, you can rewrite it as the fraction raised to that power. It's like saying "square the whole fraction" instead of "square the top and bottom separately."
Not for this type of question! When asked to find the equivalent expression, you need to match the mathematical form, not calculate the decimal value. Look for the choice that shows the same mathematical structure.
This choice represents multiplication by 2, which would equal , not . The original expression involves squaring, not multiplying by 2!
Think of it as "moving the exponent outside" the fraction. When both top and bottom have the same exponent, you can write it as the whole fraction raised to that power:
Yes! This rule works with any exponent as long as it's the same on both numerator and denominator. For example:
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