Question

someone help attachment below

Answer 1

I would use the rule: if you "flip" a fraction, you change the exponent by multiplying it by -1

Answer 2

I would also use the fact that 27= 3*3*3 = 3^3

Answer 3

I still dont understand

Answer 4

can someone explain or help me

Answer 5

@phi

Answer 6

they expect you to have learned a few rules about exponents
(1/a)^n = a^ -n
or
a^n = (1/a)^ -n

use the rule on the left side.

Answer 7

to use that rule. the first step is "flip" ⅓
can you do that? what do you get ?

Answer 8

3/1

Answer 9

yes, and we usually would just write it as 3
but when we flip it, we have to change the exponent by multiplying the exponent by -1
the exponent of (⅓)^x is +x
so after "flipping" the ⅓ you make the exponent -x
3^ -x

Answer 10

that narrows down your choices to the last two

Answer 11

okay I get that now

Answer 12

for the right side, you replace 27 with 3^3

Answer 13

okay

Answer 14

the right side becomes
\[ \left( 3^3\right)^{(x+2)} \]

Answer 15

oh okay I understand now

Answer 16

now you use another rule
\[ \left(a^b\right)^c= a^{bc}\]

which says "if you have a power to a power" then multiply they powers

Answer 17

so we plug those numbers in?

Answer 18

in other words, the new exponent is 3*(x+2)
you should "distribute" the 3 which means multiply 3 times each term inside the parens

Answer 19

so it would be 6

Answer 20

3x+6

Answer 21

3*(x+2) is not just 6
yes, it is 3x + 3*2 or 3x+6

to help remember, think of the parens as a package with "stuff" inside it. if you have 3 packages, you have 3 of each thing inside the package.

Answer 22

Okay thank you for your help

Answer 23

so the answer is the last one?

Answer 24

yes. More importantly, the answer is knowing how to do this.

Answer 25

definitely thank you