Math  /  Algebra

QuestionFind the equivalent expression for (m163)14(m^{\frac{16}{3}})^{\frac{1}{4}}. Options: a. m34\sqrt[4]{m^{3}}, b. mm34m \sqrt[4]{m^{3}}, c. mm3m \sqrt[3]{m}, d. m2m3m^{2} \sqrt[3]{m}.

Studdy Solution
We know that m1m^{1} is just mm and m13m^{\frac{1}{3}} is the cube root of mm.
m1×m13=m×m3m^{1} \times m^{\frac{1}{3}} = m \times \sqrt[3]{m} So, the equivalent expression for (m163)14\left(m^{\frac{16}{3}}\right)^{\frac{1}{4}} is mm3m \sqrt[3]{m}.
The correct answer is option c.

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