Question

Which of the following is an equivalent expression to the expression a1/3 / a1/4

A. A1/12

B. A7/12

C. 1/1/1/a12

D. 1/7/a12

Answer 1

Option A :-
`\sf {a}^{(1)/(12)}`

Explanation:

`\hookrightarrow \sf \: \frac{ {a}^{ (1)/(3) } }{ {a}^{ (1)/(4) } }`

Simplify the expression

`\hookrightarrow \sf \: {a}^{ (1)/(3) - (1)/(4) }`

Transform the Expression

`\hookrightarrow \sf \: {a}^{ (4 - 3)/(12) }`

Calculate

`\hookrightarrow \sf {a}^{(1)/(12)}`

Answer 2

Option A

Explanation:

Exponent Law: In exponent division, if base are same, subtract the powers

`\sf (a^m)/(a^n)=a^(m-n)`

`\sf (1)/(3)-(1)/(4)=(1*4)/(3*4)-(1*3)/(4*3)`

`\sf =(4)/(12)-(3)/(12)\\\\=(1)/(12)`

`\sf \frac{a^{(1)/(3)}}{a^{(1)/(4)}}=a^{(1)/(3)-(1)/(4)}`

`=a^{(1)/(12)}`