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luisejr77

Answer: First option.

Step-by-step explanation:

For this exercise it is importnatn to to remember the properties that are shown below:

1) [tex]a^\frac{1}{n}=\sqrt[n]{a}[/tex]

2) [tex](a^m)^n=a^{(mn)}[/tex]

Therefore, given the following expression provided in the exercise:

[tex]\sqrt[3]{4^5}[/tex]

You can apply the properties mentioned before, in order to find an equivalent expression.

Therefore, you get:

[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5*1}{3}}=4^{\frac{5}{3}}[/tex]

Then the answer is the first option.

isyllus

Answer:

[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}[/tex]

Option 1 and Option 3 is correct

Step-by-step explanation:

Given: [tex] 4^{\frac{5}{3}}=\sqrt[3]{4^5}[/tex]

This is exponent to radical change property.

The fraction exponent write as radical.

[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]

  • Option 1:  Radical to exponent

[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}[/tex]

True

  • Option 2: Addition of exponent if base is same.

[tex]4^{\frac{8}{3}}\cdot 4^{\frac{7}{3}}=4^{{\frac{8}{3}+\frac{7}{3}}=4^5[/tex]

False

  • Option 3: Multiply exponent to exponent, True
  • Option 4: Division property of exponent, False

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