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La raíz cúbica de \(8m^{6}n^{12}p^{21}q^{3}\) es \(2m^{2}n^{4}p^{7}q\).
Solution
Calculate or simplify the expression \( \sqrt[3]{8m^6n^{12}p^{21}q^3} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt[3]{8m^{6}n^{12}p^{21}q^{3}}\)
- step1: Transform the expression:
\(\sqrt[3]{\left(2m^{2}n^{4}p^{7}q\right)^{3}}\)
- step2: Simplify the root:
\(2m^{2}n^{4}p^{7}q\)
La raíz cúbica de \(8m^{6}n^{12}p^{21}q^{3}\) es \(2m^{2}n^{4}p^{7}q\).
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Simplify this solution Bonus Knowledge
To solve \( \sqrt[3]{8 m^{6} n^{12} p^{21} q^{3}} \), we can simplify each component inside the cube root. First, break it down: \( \sqrt[3]{8} = 2 \), because \( 2^3 = 8 \). For the variables: - \( \sqrt[3]{m^{6}} = m^{2} \) (since \( 6 \div 3 = 2 \)) - \( \sqrt[3]{n^{12}} = n^{4} \) (since \( 12 \div 3 = 4 \)) - \( \sqrt[3]{p^{21}} = p^{7} \) (since \( 21 \div 3 = 7 \)) - \( \sqrt[3]{q^{3}} = q^{1} \) (since \( 3 \div 3 = 1 \)) Now combine these results: \[ \sqrt[3]{8 m^{6} n^{12} p^{21} q^{3}} = 2 m^{2} n^{4} p^{7} q \] So the final expression is \( 2 m^{2} n^{4} p^{7} q \).
