Question

how do you get 2^(-7)=x^(5)

Answer 1

2\[2^{-7}=x^{5}\]

Answer 2

I don't think I'm understanding the problem, do you want to know how to solve for x?

Answer 3

yea

Answer 4

hmmm get teh fifth root for each side

Answer 5

huh

Answer 6

You can introduce a new exponent as long as it is done to each side. For example, (x^5)^1/5=(2^-7)^1/5

Answer 7

What would you get when you simplify that?

Answer 8

I don't know lol

Answer 9

\(\bf 2^{-7}=x^5\implies \cfrac{1}{2^7}=x^5\implies \sqrt[5]{\cfrac{1}{2^7}}=\sqrt[5]{x^5}\implies \cfrac{\sqrt[5]{1}}{\sqrt[5]{2^7}}=x
\\ \quad \\
\cfrac{1}{\sqrt[5]{2^7}}=x\implies \square ?\)

Answer 10

recall that \(\large a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\)

Answer 11

That is basically what needs to be done, now do you know how the 5th root part simplifies at the end? What I'm trying to say is do you know how to turn that into one exponent?

Answer 12

the answer at the end is 0.3789

Answer 13

I didn't check but that's not what I was asking. Write out that 5th root of 2^7 as just 2 to some power

Answer 14

This will be good practice later on when you want to keep exponents in place to make further simplification easier.

Answer 15

I don't understand. If you can use the equation bar that will help.

Answer 16

hmmm

Answer 17

\[\sqrt[5]{2^{7}} = ?\]

Answer 18

Write this as 2 to some exponent

Answer 19

4 but that's not the answer

Answer 20

http://www.math-play.com/image-exponents-rules.jpg

Answer 21

I know it's not and I feel bad for dragging this out but it will help to know these basic exponent rules

Answer 22

I know the basic exponent rules but what Jdoe did up their will not give me the correct answer

Answer 23

1/5square(2^7) equals 1/4 which is not the answer

Answer 24

I think jdoe is right though, \[1/\sqrt[5]{2^{7}}\]= x

Answer 25

it is nvm

Answer 26

Step by step:
2^-7=x^5
1/(2^7)=x^5
(1/(2^7))^1/5=x
1/(2^7)^1/5=x