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

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:

- At first change 27 to b^n

∵ 27 = 3 × 3 × 3 = 3³

∴

* Lets use rule (2)

∴ ⇒ 3 × -2/3 = -2

* Use rule (1)

∴ ⇒ reciprocal the fraction to change the sig of the power

* The answer is 1/9

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: