Answer:
The answer is 1/9 ⇒ the second answer
Step-by-step 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: [tex](27)^{-\frac{2}{3}}[/tex]
- At first change 27 to b^n
∵ 27 = 3 × 3 × 3 = 3³
∴ [tex]27^{-\frac{2}{3}}=(3^{3})^{-\frac{2}{3}}[/tex]
* Lets use rule (2)
∴ [tex]27^{-\frac{2}{3}}=3^{-2}[/tex] ⇒ 3 × -2/3 = -2
* Use rule (1)
∴ [tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex] ⇒ reciprocal the fraction to change the sig of the power
* The answer is 1/9
