Answer: 5^{11} – 9 = 5^{11} – 9
Explanation:
The problem involves evaluating an exponential expression and then performing a simple subtraction. The key concept here is understanding the properties of exponents and recognizing that the expression is straightforward: it asks for the value of 5 raised to the 11th power, minus 9. No complex theorems are necessary beyond basic exponentiation and subtraction.
Steps:
- Recognize the expression: \(5^{11} - 9\).
- Since \(5^{11}\) is an exponential expression, it remains as is unless explicitly asked to compute its numerical value.
- The expression simplifies to:
\[
5^{11} - 9
\]
- To find the exact numerical value, compute \(5^{11}\):
\[
5^{11} = 5 \times 5^{10}
\]
and \(5^{10} = (5^5)^2\).
- Calculate \(5^5\):
\[
5^5 = 5 \times 5^4 = 5 \times (5^3 \times 5) = 5 \times (125 \times 5) = 5 \times 625 = 3125
\]
- Therefore,
\[
5^{10} = (5^5)^2 = 3125^2 = 9,765,625
\]
- Now,
\[
5^{11} = 5 \times 9,765,625 = 48,828,125
\]
- Subtract 9:
\[
48,828,125 - 9 = 48,828,116
\]
Final result:
\[
\boxed{48,828,116}
\]
Note: If the question only asks for the simplified expression, the answer is simply \(5^{11} - 9\). If a numerical value is required, it is 48,828,116.