Question

PLEASE HELP! Im not very good at math

Answer 1

No the answer is incorrect.

Explanation:

From the question given;

(
`X^{(2)/(5) }` .
`X^{(4)/(5) }` /
`X^{(2)/(5) }` )¹/²

We will start by solving the inner bracket

By the law of indices
`x^(a) . x^(b) = x^(a+b)`

`X^{(2)/(5) }` .
`X^{(4)/(5) }` =
`X^{(2)/(5)+(4)/(5) } = X^{(6)/(5) }`

we will replace
`X^{(2)/(5) }` .
`X^{(4)/(5) }` by
`X^{(6)/(5) }`

`X^{(2)/(5) }` .
`X^{(4)/(5) }` by
`X^{(6)/(5) }`

(
`X^{(2)/(5) }` .
`X^{(4)/(5) }` /
`X^{(2)/(5) }` )¹/² = (
`X^{(6)/(5) }` /
`X^{(2)/(5) }` )¹/²

By the law of indices
`x^(a) /x^(b) = x^(a-b)`

`X^{(6)/(5) }` /
`X^{(2)/(5) }` =
`X^{(6)/(5) - (2)/(5) }` =
`X^{(4)/(5) }`

We will replace
`X^{(6)/(5) }` /
`X^{(2)/(5) }` by
`X^{(4)/(5) }`

(
`X^{(6)/(5) }` /
`X^{(2)/(5) }`)¹/² = (
`X^{(4)/(5) }`)¹/² =
`X^{(4)/(10) }` =
`X^{(2)/(5) }`

(
`X^{(2)/(5) }` .
`X^{(4)/(5) }` /
`X^{(2)/(5) }` )¹/² =
`X^{(2)/(5) }`

No the answer is incorrect.

He made a mistake, because
`X^{(6)/(5) }` /
`X^{(2)/(5) }` = =
`X^{(6)/(5) - (2)/(5) }` =
`X^{(4)/(5) }` and not equal to
`x^(3)`

Answer 2

The answer provided is incorrect, the mistake is in the division between the monomials
`x^{(6)/(5)}` and
`x^{(2)/(5)}` that is equal to
`x^{(4)/(5)` not
`x^3`, because we must mantain the same base "x" and subtract the expoents that are
`(6)/(5) - (2)/(5) = (4)/(5)`.

Explanation:

In order to simplify that question we need to multiply, divide and power monomials with the same base "x". When we multiply monomias with the same base we sum the expoents, to divide we subtract the expoents and to power them we multiply the expoents. Therefore to simplify the equations we must do:

`(\frac{x^{(2)/(5)}*x^{(4)/(5)}}{x^{(2)/(5)}})^(1)/(2)\\(\frac{x^{(6)/(5)}}{x^{(2)/(5)}})^(1)/(2)\\(x^{(4)/(5)})^(1)/(2)\\x^{(4)/(10)}\\x^{(2)/(5)}`

The answer provided is incorrect, the mistake is in the division between the monomials
`x^{(6)/(5)}` and
`x^{(2)/(5)}` that is equal to
`x^{(4)/(5)` not
`x^3`, because we must mantain the same base "x" and subtract the expoents that are
`(6)/(5) - (2)/(5) = (4)/(5)`.