Question

Which of the following is an equivalent expression to the expression a^1/3 divided by a^1/4?

A. 1/a^12
B. 7/a^12
C. 1/a^12
D. 1/a^7/12

Answer 1

C. 1/a¹²

Explanation:

Formula

• 
  `(a^(m))/(a^(n) ) = a^(m-n)`

Applying that here :

• 
  `\frac{a^{(1)/(3) } }{a^{(1)/(4) } } = a^{(1)/(3)-(1)/(4) }`
• 
  `a^{(4-3)/(12) } = a^{(1)/(12) }`
• 1/a¹²

Answer 2

a^1/12 or choice A

Explanation:

Given:

`\displaystyle \large{\frac{a^{(1)/(3)}}{a^{(1)/(4)}}}`

Law of Exponent (Division Property):

`\displaystyle \large{(a^m)/(a^n) = a^(m-n)}`

Therefore:

`\displaystyle \large{a^{(1)/(3)-(1)/(4)}}`

Then evaluate the fractions. Keep in mind that we can only evaluate fractions with same denominator. Therefore, calculate the LCM of 3,4 which is 12:

`\displaystyle \large{a^{(4)/(12)-(3)/(12)} = a^{(1)/(12)}}`

Therefore, the solution is a^1/12 or choice A