Respuesta :

sqdancefan

Answer:

  [tex]\sqrt[3]{5^7}[/tex]

Step-by-step explanation:

According to the rules of roots and exponents, ...

  [tex]\displaystyle \boxed{5^{7/3}=\sqrt[3]{5^7}}[/tex]

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The denominator of the fractional exponent is the index of the root. The numerator of the fractional exponent can be applied inside or outside the root:

  a^(b/c) = (a^(1/c))^b = (a^b)^(1/c)

The answer will be 3 StartRoot 5 Superscript 7 Baseline EndRoot.

3 StarRoot

The 3 StarRoot of a number is the factor that we multiply by itself three times to get that number

How to solve this problem?

The steps are as follow:

  • 5 Superscript seven-thirds can be represented as [tex]5^{\frac{7}{3} }[/tex]
  • It can also be represent as [tex][5^{7}]^\frac{1}{3} }[/tex]
  • Now as per rule of mathematics:

[tex][5^{7}]^\frac{1}{3} } = \sqrt[3]{5^{7} }[/tex]

So, 5 Superscript seven-thirds equivalents to 3 StartRoot 5 Superscript 7 Baseline EndRoot

Learn more about 3 StarRoot here:

https://brainly.com/question/14880572

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