Question

Select all rational expressions that are equivalent to ​

Answer 1

:

Answer:

and

Explanation:

Both the power and the root of a number aplied at the same time can be written or expressed in two different ways: indistinctly.

Because there is no difference in expressing the power of a number in a fractional form as shown before, the expression equals the expression .

Then, we already have two equals expressions: and .

If we take the last expression and solve , we get , which is another equal expression for the inicial.

Answer 2

`\sqrt[5]{4^3}` and
`\sqrt[5]{64}`

Explanation:

• Both the power and the root of a number aplied at the same time can be written or expressed in two different ways:
  `\sqrt[n]{x^k}=x^{(k)/(n)}` indistinctly.
• Because there is no difference in expressing the power of a number in a fractional form as shown before, the expression
  `4^{(3)/(5)}` equals the expression
  `\sqrt[5]{4^3}`.
• Then, we already have two equals expressions:
  `4^{(3)/(5)}` and
  `\sqrt[5]{4^3}`.
• If we take the last expression
  `\sqrt[5]{4^3}` and solve
  `4^3=4*4*4=64`, we get
  `\sqrt[5]{64}`, which is another equal expression for the incial
  `4^{(3)/(5)}`.