Question

simplify. assume all variables are positive. $y^{\frac{11}{7}}\div y^{\frac{3}{4}}$ write your answer in the form $a$ or $\frac{a}{b}$ where $a$ and $b$ are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Use exponent - division rule

When dividing two powers with the same base \(a^m\div a^n=a^{m - n}\), here \(a = y\), \(m=\frac{11}{7}\), and \(n=\frac{2}{3}\).
\[y^{\frac{11}{7}}\div y^{\frac{2}{3}}=y^{\frac{11}{7}-\frac{2}{3}}\]

Step2: Find a common denominator

The common denominator of 7 and 3 is 21. So \(\frac{11}{7}-\frac{2}{3}=\frac{11\times3}{7\times3}-\frac{2\times7}{3\times7}=\frac{33}{21}-\frac{14}{21}\).
\[y^{\frac{33}{21}-\frac{14}{21}}\]

Step3: Subtract the fractions

\(\frac{33}{21}-\frac{14}{21}=\frac{33 - 14}{21}=\frac{19}{21}\)
\[y^{\frac{19}{21}}\]

Answer:

\(y^{\frac{19}{21}}\)