Question

Simplify 27 to the negative 2 thirds power. 9 1 over 9 negative 1 over 9 −9

Answer 1

option 2

Explanation:

Answer 2

The answer is 1/9 ⇒ the second answer

Explanation:

* In the exponential functions we have some rules

(1) b^(-m) = 1/(b^m) (for all nonzero real numbers b)

- If we have negative power we reciprocal the base

to get positive power

(2) (b^m)^n = b^(mn)

- If we have power over power we multiply them

* In our problem:
`(27)^{-(2)/(3)}`

- At first change 27 to b^n

∵ 27 = 3 × 3 × 3 = 3³

∴
`27^{-(2)/(3)}=(3^(3))^{-(2)/(3)}`

* Lets use rule (2)

∴
`27^{-(2)/(3)}=3^(-2)` ⇒ 3 × -2/3 = -2

* Use rule (1)

∴
`3^(-2)=(1)/(3^(2))=(1)/(9)` ⇒ reciprocal the fraction to change the sig of the power

* The answer is 1/9