Answer :
Sure, let's solve each expression step by step.
### Expression 1: \(3^3 - 9 \times 3^0 - \frac{1}{3^{-4}} - \frac{1}{3^{-4}}\)
Step 1: Calculate \(3^3\).
[tex]\[ 3^3 = 27 \][/tex]
Step 2: Calculate \(9 \times 3^0\). Since \(3^0 = 1\):
[tex]\[ 9 \times 1 = 9 \][/tex]
Step 3: Calculate \(\frac{1}{3^{-4}}\). Recall that \(3^{-4} = \frac{1}{3^4} = \frac{1}{81}\), so:
[tex]\[ \frac{1}{3^{-4}} = \frac{1}{\frac{1}{81}} = 81 \][/tex]
Step 4: We need to subtract two instances of \(\frac{1}{3^{-4}}\). So:
[tex]\[ 2 \times 81 = 162 \][/tex]
Step 5: Combine all results from the above steps:
[tex]\[ 27 - 9 - 162 = -144 \][/tex]
Hence, the result of the first expression is \(-144.0\).
### Expression 2: \(3^3 - 3^2 \times 3^0 + \frac{1}{3^4} + \frac{1}{3^4}\)
Step 1: Calculate \(3^3\).
[tex]\[ 3^3 = 27 \][/tex]
Step 2: Calculate \(3^2 \times 3^0\). Since \(3^0 = 1\):
[tex]\[ 3^2 \times 1 = 9 \][/tex]
Step 3: Calculate \(\frac{1}{3^4}\). Since \(3^4 = 81\):
[tex]\[ \frac{1}{3^4} = \frac{1}{81} \][/tex]
Step 4: We need to add two instances of \(\frac{1}{3^4}\). So:
[tex]\[ \frac{1}{81} + \frac{1}{81} = \frac{2}{81} \approx 0.024691358024691 \][/tex]
Step 5: Combine all results from the above steps:
[tex]\[ 27 - 9 + \frac{2}{81} = 18 + 0.024691358024691 = 18.02469135802469 \][/tex]
Hence, the result of the second expression is \(18.02469135802469\).
So, the final answers are:
[tex]\[ \begin{array}{l} 3^3-9 \times 3^0-\frac{1}{3^{-4}}-\frac{1}{3^{-4}} = -144.0 \\ 3^3-3^2 \times 3^0+\frac{1}{3^4}+\frac{1}{3^4} = 18.02469135802469 \end{array} \][/tex]
### Expression 1: \(3^3 - 9 \times 3^0 - \frac{1}{3^{-4}} - \frac{1}{3^{-4}}\)
Step 1: Calculate \(3^3\).
[tex]\[ 3^3 = 27 \][/tex]
Step 2: Calculate \(9 \times 3^0\). Since \(3^0 = 1\):
[tex]\[ 9 \times 1 = 9 \][/tex]
Step 3: Calculate \(\frac{1}{3^{-4}}\). Recall that \(3^{-4} = \frac{1}{3^4} = \frac{1}{81}\), so:
[tex]\[ \frac{1}{3^{-4}} = \frac{1}{\frac{1}{81}} = 81 \][/tex]
Step 4: We need to subtract two instances of \(\frac{1}{3^{-4}}\). So:
[tex]\[ 2 \times 81 = 162 \][/tex]
Step 5: Combine all results from the above steps:
[tex]\[ 27 - 9 - 162 = -144 \][/tex]
Hence, the result of the first expression is \(-144.0\).
### Expression 2: \(3^3 - 3^2 \times 3^0 + \frac{1}{3^4} + \frac{1}{3^4}\)
Step 1: Calculate \(3^3\).
[tex]\[ 3^3 = 27 \][/tex]
Step 2: Calculate \(3^2 \times 3^0\). Since \(3^0 = 1\):
[tex]\[ 3^2 \times 1 = 9 \][/tex]
Step 3: Calculate \(\frac{1}{3^4}\). Since \(3^4 = 81\):
[tex]\[ \frac{1}{3^4} = \frac{1}{81} \][/tex]
Step 4: We need to add two instances of \(\frac{1}{3^4}\). So:
[tex]\[ \frac{1}{81} + \frac{1}{81} = \frac{2}{81} \approx 0.024691358024691 \][/tex]
Step 5: Combine all results from the above steps:
[tex]\[ 27 - 9 + \frac{2}{81} = 18 + 0.024691358024691 = 18.02469135802469 \][/tex]
Hence, the result of the second expression is \(18.02469135802469\).
So, the final answers are:
[tex]\[ \begin{array}{l} 3^3-9 \times 3^0-\frac{1}{3^{-4}}-\frac{1}{3^{-4}} = -144.0 \\ 3^3-3^2 \times 3^0+\frac{1}{3^4}+\frac{1}{3^4} = 18.02469135802469 \end{array} \][/tex]
