Please help and look at the picture

Question

asked Aug 20, 2020 198k views

1 Answer

Won Chul Jo · Answer 1 · 2020-08-25T15:00:02+0000

ANSWER

A.

(1)/(64)

Step-by-step explanation

The given expression is:

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) }$

Recall that:

${a}^(m) / {a}^(n) = {a}^(m - n)$

We apply this property to obtain:

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) } = {4}^{ - (11)/(3) - - (2)/(3) }$

Collect LCM

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) } = {4}^{ ( - 11 + 3)/(3)}$

Simplify;

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) } = {4}^{ ( - 9)/(3)}$

.

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) } = {4}^( - 3)$

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) } = \frac{1}{ {4}^(3) }$

${4}^{ - (11)/(3) } / {4}^{ - (2)/(3) } = (1)/(64)$

The first choice is correct