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Answer
The simplified form of \( \frac{5^{n+4}}{5^{n+5}} \) is \( \frac{1}{5} \).
Solution
To simplify the expression (5^(n+4))/(5^(n+5)), use the rule for dividing exponential expressions with the same base, which states that a^(m) / a^(n) = a^(m - n).
Step 1: Write the expression with the subtraction of exponents:
(5^(n+4))/(5^(n+5)) = 5^[(n+4) - (n+5)].
Step 2: Simplify the exponent:
(n+4) - (n+5) = n + 4 - n - 5 = -1.
Step 3: Express the result with the simplified exponent:
5^(-1) = 1/5.
Thus, the final answer is 1/5.
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Simplify this solution The Deep Dive
To simplify \( \frac{5^{n+4}}{5^{n+5}} \), we can use the laws of exponents. When dividing two expressions with the same base, we subtract the exponents. This gives us: \[ \frac{5^{n+4}}{5^{n+5}} = 5^{(n+4)-(n+5)} = 5^{n+4-n-5} = 5^{-1} \] Thus, we have \( 5^{-1} = \frac{1}{5} \). So, the simplified form of the original expression is \( \frac{1}{5} \).
