Respuesta :


[tex]( \sqrt[4]{ {5}^{3} } ) = {5}^{ \frac{3}{4} } [/tex]
Power over root

[tex]( {5}^{ \frac{3}{4} } ) ^{ \frac{1}{2} } [/tex]
Multiple the exponents and that's your answer!
Speedbird1

Answer:

(C) [tex]5^{\frac{3}{8} }[/tex]

Step-by-step explanation:

With a calculator, this would be pretty straightforward, but if not, there is an easy way to go about it:

  1. Convert your fourth root to an exponent and use the exponent rule: [tex](5^{3})^{\frac{1}{4}*\frac{1}{2}  }[/tex]
  2. Simplify with the exponent rule: ([tex]\frac{1}{4}[/tex] * [tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{8}[/tex] = ([tex]5^{3}[/tex])[tex]^{\frac{1}{8} }[/tex]
  3. Apply the exponent rule once more: 3 * [tex]\frac{1}{8}[/tex] = [tex]\frac{3}{8}[/tex]

And now, the answer is in the simplest of forms. If you have a calculator, this can easily be inserted to find the decimal value of it.

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