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

2 Answers

5 votes

Answer:

option 2

Explanation:

User Jaanhio
by
4.8k points
5 votes

Answer:

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

User Alesanco
by
5.2k points