ANSWER
A.
[tex] \frac{1}{64} [/tex]
EXPLANATION
The given expression is:
[tex] {4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } [/tex]
Recall that:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
We apply this property to obtain:
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - \frac{11}{3} - - \frac{2}{3} } [/tex]
Collect LCM
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 11 + 3}{3}} [/tex]
Simplify;
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 9}{3}} [/tex]
.
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - 3} [/tex]
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{ {4}^{3} } [/tex]
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{64} [/tex]
The first choice is correct
