Question

Please help! Please explain what a integer exponent means and what’s the answer

Answer 1

Number 4

Explanation:

Using the rule of radicals/ exponents

`\sqrt[n]{x^(m) }` ⇔
`x^{(m)/(n) }`

An integer is a whole number including negative numbers and zero

Z = { ..... - 3, - 2, - 1, 0, 1, 2, 3, .......... }

Consider each in turn using the above rule

(1)

`\sqrt[4]{x^(9) }` =
`x^{(9)/(4) }` ← exponent is not an integer

(2)

`\sqrt[10]{x^(12) }` =
`x^{(12)/(10) }` ← exponent is not an integer

(3)

`\sqrt[12]{x^(18) }` =
`x^{(18)/(12) }` ← exponent is not an integer

(4)

`\sqrt[5]{x^(10) }` =
`x^{(10)/(5) }` = x² ← exponent simplifies to an integer