ANSWER
B. 81
EXPLANATION
The given expression is:
[tex] {3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } [/tex]
Recall that:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
We simplify the expression using the properties of exponents to obtain:
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11}{5} - - \frac{9}{5} } [/tex]
We simplify the exponents to get;
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11 + 9}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{20}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{4} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = 81[/tex]
The correct answer is B. 81
