Question

assignment 2: problem 1 (1 point) rewrite the following expressions using just one rational exponent. enter the numerator and denominator of the exponent. cancel any common factors. $\frac{u^{\frac{7}{2}}u^{\frac{1}{4}}}{u^{\frac{1}{3}}u^{\frac{17}{12}}}=u^{\frac{a}{b}}$ where $a = 0$ and $b = 1$. $\frac{u^{\frac{15}{4}}u^{\frac{1}{3}}}{u^{\frac{1}{2}}u^{\frac{19}{12}}}=u^{\frac{a}{b}}$ where $a = 7$ and $b = 24$. hint: put together what you learned in the preceding few problems. note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 1 time. your overall recorded score is 25%. you have unlimited attempts remaining.

Explanation:

Step1: Use exponent - addition rule

$\frac{u^{\frac{7}{2}}u^{\frac{1}{4}}}{u^{\frac{1}{3}}u^{\frac{17}{12}}}=u^{\frac{7}{2}+\frac{1}{4}-\frac{1}{3}-\frac{17}{12}}$

Step2: Find common denominator

$u^{\frac{42 + 3- 4 - 17}{12}}=u^{\frac{24}{12}}=u^{2}$

Step3: For second expression

$\frac{u^{\frac{15}{4}}u^{\frac{1}{3}}}{u^{\frac{1}{2}}u^{\frac{19}{12}}}=u^{\frac{15}{4}+\frac{1}{3}-\frac{1}{2}-\frac{19}{12}}$

Step4: Calculate exponent

$u^{\frac{45+4 - 6 - 19}{12}}=u^{\frac{24}{12}} = u^{2}$

Answer:

For first: $a = 2$, $b = 1$; For second: $a = 2$, $b = 1$