anonymous
  • anonymous
Rewrite the rational exponent as a radical. 5 to the 3 over 4 power, to the 2 over 3 power
Algebra
chestercat
  • chestercat
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jdoe0001
  • jdoe0001
\(\large \left( 5^{\frac{3}{4}} \right)^{\frac{2}{3}} ?\)
anonymous
  • anonymous
yes
jdoe0001
  • jdoe0001
anyhow, keep in mind that \(\bf (a^n)^m\implies a^{n\cdot m}\qquad and\qquad a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\)

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anonymous
  • anonymous
thanks
jdoe0001
  • jdoe0001
thus \(\large \bf \left( 5^{\frac{3}{4}} \right)^{\frac{2}{3}}\implies 5^{\frac{3}{4}\cdot \frac{2}{3}}\implies 5^{\frac{{\color{blue}{ 3\cdot 2 }}}{{\color{red}{4\cdot 3 }}}}\)
anonymous
  • anonymous
so after you multiply the exponents do you put it back in that form at the top^

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