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

Answer:

C. 1/a¹²

Step-by-step explanation:

Formula

• $\frac{a^{m}}{a^{n} } = a^{m-n}$

Applying that here :

• $\frac{a^{\frac{1}{3} } }{a^{\frac{1}{4} } } = a^{\frac{1}{3}-\frac{1}{4} }$
• $a^{\frac{4-3}{12} } = a^{\frac{1}{12} }$
• 1/a¹²

Answer 2

Answer:

a^1/12 or choice A

Step-by-step explanation:

Given:

$\displaystyle \large{\dfrac{a^{\dfrac{1}{3}}}{a^{\dfrac{1}{4}}}}$

Law of Exponent (Division Property):

$\displaystyle \large{\dfrac{a^m}{a^n} = a^{m-n}}$

Therefore:

$\displaystyle \large{a^{\dfrac{1}{3}-\dfrac{1}{4}}}$

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:

$\displaystyle \large{a^{\dfrac{4}{12}-\dfrac{3}{12}} = a^{\dfrac{1}{12}}}$

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