james1769
  • james1769
Describe how to transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent. Make sure you respond with complete sentences.
Mathematics
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SOLVED
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chestercat
  • chestercat
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Michele_Laino
  • Michele_Laino
please keep in mind that the radical: \[\sqrt[3]{{{x^4}}}\] can be rewritten as below: \[{x^{4/3}}\]
Michele_Laino
  • Michele_Laino
it is the definition of powers with rational exponent
Michele_Laino
  • Michele_Laino
now, if I apply the rule of power of power, we can write this: \[\huge{\left( {\sqrt[3]{{{x^4}}}} \right)^5} = {\left( {{x^{4/3}}} \right)^5} = {x^{5 \cdot \frac{4}{3}}} = {x^{\frac{{20}}{3}}}\]

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Michele_Laino
  • Michele_Laino
\[\Large {\left( {\sqrt[3]{{{x^4}}}} \right)^5} = {\left( {{x^{4/3}}} \right)^5} = {x^{5 \cdot \frac{4}{3}}} = {x^{\frac{{20}}{3}}}\]
james1769
  • james1769
okay thnks
Michele_Laino
  • Michele_Laino
:)

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