Question
Simplify the expression. Write the answer with positive exponents only. Assume all variables represent nonzero real numbers. \[ \frac{m^{-6} n^{-6}}{m^{0} n^{9}}= \]
Ask by Chadwick Chen. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{1}{m^{6}n^{15}} \).
Solution
Calculate or simplify the expression \( \frac{m^{-6} n^{-6}}{m^{0} n^{9}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{m^{-6}n^{-6}}{m^{0}n^{9}}\)
- step1: Multiply by \(a^{-n}:\)
\(m^{-6}n^{-6}m^{0}n^{-9}\)
- step2: Evaluate the power:
\(m^{-6}n^{-6}\times 1\times n^{-9}\)
- step3: Rewrite the expression:
\(m^{-6}n^{-6}\times n^{-9}\)
- step4: Multiply the terms:
\(m^{-6}n^{-6-9}\)
- step5: Subtract the numbers:
\(m^{-6}n^{-15}\)
- step6: Simplify:
\(\frac{1}{m^{6}n^{15}}\)
The simplified expression is \(\frac{1}{m^{6}n^{15}}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To simplify the expression \(\frac{m^{-6} n^{-6}}{m^{0} n^{9}}\), start by applying the properties of exponents. We know that \(m^{0} = 1\), so the expression becomes \(\frac{m^{-6} n^{-6}}{1 \cdot n^{9}}\) or simply \(\frac{m^{-6} n^{-6}}{n^{9}}\). Now, simplifying the \(n\) terms in the denominator and the numerator gives us: \[ m^{-6} n^{-6} \cdot n^{-9} = m^{-6} n^{-6 - 9} = m^{-6} n^{-15} \] Next, we convert negative exponents to positive exponents by using the property that \(a^{-b} = \frac{1}{a^b}\): \[ m^{-6} n^{-15} = \frac{1}{m^{6} n^{15}} \] Thus, the simplified expression with positive exponents is: \[ \frac{1}{m^{6} n^{15}} \]
