Question

(X-4)^3/2=27

Answer 1

@amistre64

Answer 2

Or anyone :)

Answer 3

is 3/2 a fraction

Answer 4

Yeah

Answer 5

ok

Answer 6

Square both sides. That will get rid of the 1/2 in the exponent.
Then take the cube root on both sides.
Solve for x.

Answer 7

cube roots both side I think @aum meant

Answer 8

yep... :P

Answer 9

\[
(x-4)^{3/2} = 27 = 3^3 \\
\text{Square both sides: } \\
(x-4)^3 = 3^6 \\
\text{Take cube root on both sides: } \\
(x-4) = (3^6)^{1/3} = 3^2 = 9 \\
x = 9 + 4 = 13
\]

Answer 10

Would you get the same answer if you just multiplied the exponent (3/2) by the reciprocal on the left side and set 27with a power of 2/3's?
(X-4)^3/2(2/3)=27^2/3
X-4=9
=13?

Answer 11

Same answer, slightly different method.

Answer 12

Alright will that same method work with other problems like this? Or is your way "safer"

Answer 13

Either method will work with similar problems. The object is to isolate x. I did it in steps to make it clear. But this problem can be done mentally without having to write/type anything down.

Answer 14

Okay. So for a problem like 6x^5/2-12=0
Would you first begin by adding 12 to the right side then divide by 6?

Answer 15

Yes.

Answer 16

So once you're left with x^5/2=2 where would I go from there?

Answer 17

Using your method, raise both sides to the power of 2/5.

Answer 18

I get a decimal when I put it in my calculator

Answer 19

\[
x = 2^{2/5} = (2^2)^{1/5} = 4^{1/5} = \sqrt[5]{4}
\]

Answer 20

Instead of decimal approximation (unless they ask you to do), leave it in the exact form as the fifth root of 4.

Answer 21

Okay thanks

Answer 22

Have patience please but, how do you get (2^ 2) ^1/5?

Answer 23

\[\large a^{mn} = (a^m)^n = (a^n)^m \]\[\large 2^{2/5} = (2)^{2 * 1/5} = (2^2)^{1/5} = 4^{1/5}
\]

Answer 24

Thanks

Answer 25

You are welcome.