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The simplified form of the expression is
.
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Beyond the Answer
This expression is a fun exercise in simplifying and understanding the behavior of exponents! First, recognize that
can be rewritten as
, and
translates to
. This means the numerator has a common base, making for easier manipulation. In the denominator,
equals
and
becomes
, helping to rewrite the overall expression in a consistent base which can reveal insights about its properties!
Now, if you’re tackling this problem, one common mistake people make is forgetting to properly handle negative exponents. Negative exponents indicate a reciprocal, so instead of disregarding them, it’s key to remember they flip your base to the denominator! By keeping careful track of the base changes and performing proper simplifications, you’ll avoid common pitfalls, leading to a successful evaluation of the expression!