Question
Simplify. \[ \frac{x^{-5}}{x^{5}} \] Write your answer with a positive exponent only.
Ask by Wyatt Cook. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{1}{x^{10}} \).
Solution
To simplify the expression, use the rule for dividing powers of the same base:
a^m / a^n = a^(m - n).
Here, m = -5 and n = 5. So, we get:
x^(-5) / x^(5) = x^(-5 - 5) = x^(-10).
Since we need the answer with only positive exponents, rewrite x^(-10) as:
1/x^(10).
Thus, the simplified expression is:
1/x^(10).
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{x^{-5}}{x^{5}} \), we can use the properties of exponents. Specifically, when we divide powers with the same base, we subtract the exponents. Therefore, we have: \[ \frac{x^{-5}}{x^{5}} = x^{-5 - 5} = x^{-10}. \] To write the answer with a positive exponent, we recall that \( x^{-n} = \frac{1}{x^{n}} \). Consequently, we can express \( x^{-10} \) as: \[ x^{-10} = \frac{1}{x^{10}}. \] So, the final answer is: \[ \frac{1}{x^{10}}. \]
