Answer: Choice A) [tex]b^{5/12}[/tex]
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Work Shown:
[tex]\frac{\sqrt[3]{b^2}}{\sqrt[4]{b}}\\\\\\\frac{b^{2/3}}{b^{1/4}}\\\\\\b^{2/3 - 1/4}\\\\\\b^{8/12 - 3/12}\\\\\\b^{5/12}\\\\\\[/tex]
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Explanation:
- In the second step, I converted from radical form to rational exponent form. The rule is [tex]\sqrt[n]{x^m} = x^{m/n}[/tex]
- In the third step, I subtracted the exponents through the rule [tex]\frac{a^b}{a^c} = a^{b-c}[/tex] where 'a' is nonzero.
- The answer is equivalent to [tex]\sqrt[12]{b^5}[/tex] which is the 12th root of b^5.
