Question

For x = 0, which expressions are equivalent to one divided by the sixth root of x?

13
1.
.
III.
1.
I and II, only
.
2.
I and III, only
3.
3.
II and III, only
4.
I, II, and III

Answer 1

4. I, II and III

Explanation:

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I.

`\huge\frac{\sqrt[6]{x}}{\sqrt[3]{x}}`

`\huge=\frac{x^{(1)/(6)}}{x^{(1)/(3)}}`

`\huge=\frac{1}{x^{(1)/(3)-(1)/(6)} }`

`\huge=\frac{1}{x^{(2)/(6)-(1)/(6)} }`

`\huge=\frac{1}{x^{(2-1)/(6)} }`

`\huge=\frac{1}{x^{(1)/(6)} }`

II.

`\huge\frac{x^{(1)/(6)}}{x^{(1)/(3)}}`

`\huge=\frac{1}{x^{(1)/(3)-(1)/(6)} }`

`\huge=\frac{1}{x^{(2)/(6)-(1)/(6)} }`

`\huge=\frac{1}{x^{(2-1)/(6)} }`

`\huge=\frac{1}{x^{(1)/(6)} }`

III

`\huge x^{-(1)/(6)}`

`\huge=\frac{1}{x^{(1)/(6)} }`