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La expresión simplifica a \( -1000m^{9}n^{6} \).
Solution
Calculate or simplify the expression \( (-10m^3n^2)^3 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-10m^{3}n^{2}\right)^{3}\)
- step1: Determine the sign:
\(-\left(10m^{3}n^{2}\right)^{3}\)
- step2: Use the properties of exponents:
\(-10^{3}\left(m^{3}\right)^{3}\left(n^{2}\right)^{3}\)
- step3: Evaluate the power:
\(-1000m^{9}n^{6}\)
La expresión \( \left(-10 m^{3} n^{2}\right)^{3} \) se simplifica a \( -1000m^{9}n^{6} \).
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Simplify this solution Bonus Knowledge
To simplify \( \left(-10 m^{3} n^{2}\right)^{3} \), we will use the power of a product rule, which states that \( (abc)^n = a^n b^n c^n \). First, we will raise each factor to the third power: \[ (-10)^3 = -1000,\quad (m^{3})^3 = m^{9},\quad (n^{2})^3 = n^{6}. \] Now, putting it all together: \[ \left(-10 m^{3} n^{2}\right)^{3} = -1000 m^{9} n^{6}. \] Thus, the simplified result is: \[ -1000 m^{9} n^{6}. \]
