Question
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Answer
A expressão simplificada é \( 0 \).
Solution
Para resolver a expressão dada, vamos calcular cada termo separadamente e depois somá-los.
1. \( 27^{-1} \):
\( 27^{-1} = \frac{1}{27} \)
2. \( (-9)^{-2} \):
\( (-9)^{-2} = \frac{1}{(-9)^2} = \frac{1}{81} \)
3. \( -3^{-3} \):
\( -3^{-3} = -\frac{1}{3^3} = -\frac{1}{27} \)
4. \( (-3)^{-4} \):
\( (-3)^{-4} = \frac{1}{(-3)^4} = \frac{1}{81} \)
Agora, vamos somar esses termos:
\( \frac{1}{27} + \frac{1}{81} - \frac{1}{27} - \frac{1}{81} \)
Vamos simplificar essa expressão:
Calculate the value by following steps:
- step0: Calculate:
\(\frac{1}{27}+\frac{1}{81}-\frac{1}{27}-\frac{1}{81}\)
- step1: Simplify:
\(\frac{1}{81}-\frac{1}{81}\)
- step2: Subtract the terms:
\(0\)
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Simplify this solution Beyond the Answer
To solve \( 27^{-1}+(-9)^{-2}-3^{-3}-(-3)^{-4} \), let’s break it down term by term: 1. \( 27^{-1} = \frac{1}{27} \) 2. \( (-9)^{-2} = \frac{1}{(-9)^2} = \frac{1}{81} \) 3. \( -3^{-3} = -\frac{1}{3^3} = -\frac{1}{27} \) 4. \( -(-3)^{-4} = -\frac{1}{(-3)^4} = -\frac{1}{81} \) Now combining these: \[ \frac{1}{27} + \frac{1}{81} - \frac{1}{27} - \frac{1}{81} \] Notice that \( \frac{1}{27} \) and \( -\frac{1}{27} \) cancel each other out, and \( \frac{1}{81} \) and \( -\frac{1}{81} \) also cancel out. Therefore, the expression simplifies to: \[ 0 \] So, the final answer is \( 0 \).
