Insert the corresponding expression:
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Insert the corresponding expression:
To solve the problem, we will follow these steps:
Now, let's work through each step:
Step 1: We start with the problem expression . According to the laws of exponents, a negative exponent means the reciprocal of the base should be raised to the positive of that exponent.
Step 2: Take the reciprocal of , which is .
Step 3: Raise the reciprocal to the power of 5, resulting in .
Therefore, the equivalent expression is .
\( \)Choose the corresponding expression:
\( \left(\frac{1}{2}\right)^2= \)
A negative exponent means "one over" the positive power. So . When your base is already a fraction, taking the reciprocal flips it!
Not usually! Most problems ask for the equivalent expression, which means keeping it as rather than computing the huge number.
Then you'd keep the fraction as-is! stays exactly that way. Only negative exponents require flipping the fraction.
No! Once you flip the fraction, the exponent becomes positive. , not .
Think "opposite"! If the original fraction is smaller than 1 (like 10/17), flipping makes it larger than 1 (17/10). The negative exponent transforms to its opposite behavior.
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