Question

question 1-12
simplify the expression: \\(\frac{c^{\frac{3}{4}}}{c^{\frac{1}{3}}}\\)
\\(\circ\\) \\(\frac{1}{c^2}\\)
\\(\circ\\) \\(c^{\frac{5}{12}}\\)
\\(\circ\\) \\(c^{\frac{13}{12}}\\)
\\(\circ\\) \\(c^1\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we subtract the exponents: \( \frac{a^m}{a^n}=a^{m - n} \). Here, the base is \( c \), so we apply this rule.
The expression is \( \frac{c^{\frac{3}{4}}}{c^{\frac{1}{3}}} \), so we subtract the exponents: \( \frac{3}{4}-\frac{1}{3} \).

Step2: Find a common denominator and subtract

The common denominator of 4 and 3 is 12. Convert \( \frac{3}{4} \) to twelfths: \( \frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12} \). Convert \( \frac{1}{3} \) to twelfths: \( \frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12} \). Now subtract: \( \frac{9}{12}-\frac{4}{12}=\frac{5}{12} \). So the simplified expression is \( c^{\frac{5}{12}} \).

Answer:

\( c^{\frac{5}{12}} \) (corresponding to the option with \( c^{\frac{5}{12}} \))