Question

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

Answer 1

Answer:

Option A

Step-by-step explanation:

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

$\sf \dfrac{a^m}{a^n}=a^{m-n}$

$\sf \dfrac{1}{3}-\dfrac{1}{4}=\dfrac{1*4}{3*4}-\dfrac{1*3}{4*3}$

          $\sf =\dfrac{4}{12}-\dfrac{3}{12}\\\\=\dfrac{1}{12}$

$\sf \dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{4}}}=a^{\frac{1}{3}-\frac{1}{4}}$

     $=a^{\frac{1}{12}}$

Answer 2

Answer:

Option A :- $\sf {a}^{\frac{1}{12}}$

Step-by-step explanation:

$\hookrightarrow \sf \: \frac{ {a}^{ \frac{1}{3} } }{ {a}^{ \frac{1}{4} } }$

Simplify the expression

$\hookrightarrow \sf \: {a}^{ \frac{1}{3} - \frac{1}{4} }$

Transform the Expression

$\hookrightarrow \sf \: {a}^{ \frac{4 - 3}{12} }$

Calculate

$\hookrightarrow \sf {a}^{\frac{1}{12}}$