Question

Please help and look at the picture

Answer 1

ANSWER

A.

$\frac{1}{64}$

EXPLANATION

The given expression is:

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} }$

Recall that:

${a}^{m} \div {a}^{n} = {a}^{m - n}$

We apply this property to obtain:

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - \frac{11}{3} - - \frac{2}{3} }$

Collect LCM

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 11 + 3}{3}}$

Simplify;

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 9}{3}}$

.

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - 3}$

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{ {4}^{3} }$

${4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{64}$

The first choice is correct