# Thread: Trouble with exponential equations

1. ## Trouble with exponential equations

The problem in particular I'm having trouble with is $\displaystyle x^(-2/3) = (1/4)$.

I think I did everything correctly when I got stuck at $\displaystyle x^1 = (1/4)^(-3/2)$

Since I'm new to the MATH tags, that's supposed to be:

x^(-2/3) = (1/4)
and
x^1 = (1/4)^(-3/2), respectively.

Would I continue on to $\displaystyle x = 4^(2/3)$ (x = 4^(2/3))which would be simple from there, or another method?

2. Originally Posted by fkhnksaha
The problem in particular I'm having trouble with is $\displaystyle x^(-2/3) = (1/4)$.

I think I did everything correctly when I got stuck at $\displaystyle x^1 = (1/4)^(-3/2)$

Since I'm new to the MATH tags, that's supposed to be:

x^(-2/3) = (1/4)
and
x^1 = (1/4)^(-3/2), respectively.

Would I continue on to $\displaystyle x = 4^(2/3)$ (x = 4^(2/3))which would be simple from there, or another method?
$\displaystyle \left(\frac{1}{4}\right)^{-3/2} = \left(4^{-1}\right)^{-3/2} = 4^{3/2} = \left(4^{1/2}\right)^3 = 2^3 = 8$.

3. Thanks a million for the quick reply! This definitely helped my understanding of reciprocals and negative exponents!