Question

Simplify the following expression.

A. 64
B. 12
C. 1/12
D. 1/64​

Answer 1

We have

`a^b\cdot a^c=a^(b+c)`

`a^b/ a^c=a^(b-c)`

So, in your case, we have

`4^{-(11)/(3)}/ 4^{-(2)/(3)} = 4^{-(11)/(3)+(2)/(3)} = 4^{-(9)/(3)}=4^(-3) = (1)/(4^3) = (1)/(64)`

Answer 2

Option D. 1/64

Explanation:

We have to simplify the following expression

`4^{-(11)/(3) }` ÷
`4^{-(2)/(3) }`

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

=
`[4^{-(11)/(3)}` ×
`4^{(2)/(3)}]` [since
`(1)/(A-1)`=a]

=
`4^{(-(11)/(3)+(2)/(3))}` [since
`a^(b)` ×
`a^(c)` =
`a^((b+c))`]

=
`4^{-(9)/(3)}`

=
`4^(-3)`

=
`(1)/(4^(3) )` [
`a^(-1)=(1)/(a)`]

=
`(1)/(64)`

Option D. 1/64 is the answer.