# Solve for X

• Nov 18th 2009, 09:14 PM
hovermet
Solve for X
Help, Solve for X
4x^-2/3 = 16

i got to the point where 1/3\sqrt{4x^2} = 16 , then i am totally lost (Sadsmile)

Also what is the rule for a base with a power of negative fraction? Why do you have to flip ex: x^-1/2. 1/\sqrt{x}

Thank You

PS: am i posting in the corrct subforum？。。.
• Nov 18th 2009, 09:22 PM
pickslides
I believe this is the correct sub forum

Can you please confirm the problem?

$4x^{-2/3} = 16$

or

$(4x)^{-2/3} = 16$
• Nov 18th 2009, 09:43 PM
hovermet
Quote:

Originally Posted by pickslides
I believe this is the correct sub forum

Can you please confirm the problem?

$4x^{-2/3} = 16$

or

$(4x)^{-2/3} = 16$

It is the top one $4x^{-2/3} = 16$ , but do you mind demonstrating the bottom one also? ty
• Nov 18th 2009, 09:53 PM
Billyboy
Use the properties of exponentiation.

solving both ways...

$
(4x)^{-2/3} = 16
$

$
(4x) = 16^{-3/2}
$

$
x = (16^{-3/2})/4
$

$
4x^{-2/3} = 16
$

$
x = (16/4)^{-3/2}
$
• Nov 18th 2009, 10:04 PM
hovermet
Quote:

Originally Posted by Billyboy
Use the properties of exponentiation.

solving both ways...

$
(4x)^{-2/3} = 16
$

$
(4x) = 16^{-3/2}
$

$
x = (16^{-3/2})/4
$

$
4x^{-2/3} = 16
$

$
x = (16/4)^{-3/2}
$

Thank You Billy, the answer key for 4x^{-2/3} = 16 is 1/8, how do you simplify it into 1/8?.. i am having big problems with negative fraction powers(Bow)
• Nov 18th 2009, 10:24 PM
Billyboy
$
x = (16/4)^{-3/2}
$

$
x = 4^{-3/2}
$

raising a nonzero number to a "−" power produces its reciprocal...

$
x^{-1} = 1/x
$

and

$
x^{-2}=1/x^2
$

i.e.

$
x^{-a}=1/x^a
$

think you get the idea...

...taking what you know from above and understanding that the numerator raises the number to that power (in this case ^3) and the denominator takes the root (in this case 2nd root or sqrt) therefore you can simplify...

...This

$
x = 4^{-3/2}
$

is the same as this...

$
x = 1/(4^{3/2})
$

is the same as this...

$
x = 1/sqrt(4^3)
$

Therefore, we easily solve...

$
4^3 = 64
$

and

$
sqrt(64) = 8
$

Thus you get...

$
x = 1/8
$
• Nov 18th 2009, 11:18 PM
Billyboy
a good property to know...

$
(a/b)^{-1} = b/a
$

Also, take for example:

$
x^{a}=y
$

to solve for x...

$
x^{a(a^{-1})}=y^{(a^{-1})}
$

$
(a*a^{-1} = a * 1/a = 1)
$

sooo...

$
x = y^{1/a}
$