Question
Rewrite \( \sqrt[3]{m^{4}} \) in simplest form.
Ask by Martinez Carrillo. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of \( \sqrt[3]{m^{4}} \) is \( m \cdot \sqrt[3]{m} \).
Solution
To simplify the expression √[3](m⁴), we start by expressing m⁴ as a product of a perfect cube and another factor. Notice that:
m⁴ = m³ · m
Taking the cube root of both factors separately gives:
√[3](m⁴) = √[3](m³ · m) = √[3](m³) · √[3](m) = m · √[3](m)
Thus, the simplified form of √[3](m⁴) is:
m · √[3](m)
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Simplify this solution Extra Insights
To simplify \( \sqrt[3]{m^{4}} \), we can use the property of exponents. We can express \( m^{4} \) as \( m^{3} \cdot m^{1} \). Thus, \[ \sqrt[3]{m^{4}} = \sqrt[3]{m^{3} \cdot m^{1}} = \sqrt[3]{m^{3}} \cdot \sqrt[3]{m^{1}} = m \cdot m^{1/3} = m^{1 + 1/3} = m^{4/3}. \] So, \( \sqrt[3]{m^{4}} \) in simplest form is \( m^{4/3} \).
