Math Help - equations involving rational exponents problem

1. equations involving rational exponents problem

(t - 1) ^-2/3 = 2

the answer is {4 - sqrt of 2 / 4}, {4 + sqrt of 2 / 4}

my steps:

1. raise each side a neg 3 to elimate neg 2

2. the 2 becomes 1/8

3. apply even root property

t-1 = + or - 1 / 2 times sq rt of 2 and from there i know i srewed up, any tips would be great

Try this way

3. Re: equations involving rational exponents problem

i dont get how you went from step 2 to 3

4. Re: equations involving rational exponents problem

Here it is in more detail

5. Re: equations involving rational exponents problem

Originally Posted by mathmathmathmathmathmathm
(t - 1) ^-2/3 = 2

the answer is {4 - sqrt of 2 / 4}, {4 + sqrt of 2 / 4}

my steps:

1. Raise each side a neg 3 to elimate neg 2

2. The 2 becomes 1/8

3. Apply even root property

t-1 = + or - 1 / 2 times sq rt of 2 and from there i know i srewed up, any tips would be great
hi all

6. Re: equations involving rational exponents problem

Originally Posted by mathmathmathmathmathmathm
(t - 1) ^-2/3 = 2

the answer is {4 - sqrt of 2 / 4}, {4 + sqrt of 2 / 4}

my steps:

1. raise each side a neg 3 to eliminate neg 2

2. the 2 becomes 1/8

3. apply even root property

t-1 = + or - 1 / (2 times sq rt of 2) and from there i know i screwed up. Any tips would be great.
The method in your Original Post looks fine as far as you went, with the addition of the above parentheses.

$t-1=\pm\frac{1}{2\sqrt{2}}$
$=\pm\frac{\sqrt{2}}{4}$
Therefore, $t=1\pm\frac{\sqrt{2}}{4}\,.$