-3

So I have this equation:

$${\left(\left(\frac{w}{x}\right)^{\frac{y}{x}}\right)}^{\frac{z}{x}}$$

And I know that

$${\left(a^b\right)}^c = a^{bc}$$

So I figured I'd simplify it into this:

$$\left(\frac{w}{x}\right)^{\frac{y}{x}\frac{z}{x}}$$

And then further into this:

$$\left(\frac{w}{x}\right)^{\frac{yz}{x^2}}$$

But for some reason, it doesn't appear to be working in all cases. What did I do wrong?

EDIT: In response to the Unclear what you're asking close votes, I am requesting assistance in finding the error in my simplification.

warspyking
  • 779
  • 1
    It's not true that $a^{b^c}=a^{b\cdot c}$, for instance, take $a=3,b=2,c=3$, we have $a^{b^c}=2^8=256$ but $a^{b\cdot c}=2^6=64$. –  Dec 17 '15 at 01:42
  • 3
    Your use of $x^{y^z}$ is ambiguous. It may mean $x^{\left(y^z\right)}$ or $\left(x^y\right)^z$. Most mathematicians use the former sense but you seem to be using it in the latter sense – Henry Dec 17 '15 at 01:44
  • @Mathos http://postimg.org/image/v1tefp7rr/ https://www.mathsisfun.com/algebra/exponent-laws.html – warspyking Dec 17 '15 at 01:45
  • @Henry that's probably my problem. I am evaluating it from left to right – warspyking Dec 17 '15 at 01:46
  • Also $\dfrac{y}{x} \times \dfrac{z}{x} \not = \dfrac{yz}{2x}$ unless $x=2$ or $yz=0$ – Henry Dec 17 '15 at 01:47
  • @Henry Okay that's my fault, but it still doesn't always work out (editing the question...) – warspyking Dec 17 '15 at 01:48
  • @Mathos, that is not the question. The question is $(a^b)^c=a^{bc}$. – Simply Beautiful Art Dec 17 '15 at 01:53

1 Answers1

1

The problem most likely occurs in the way you are calculating your answers.

In general, a calculator will provide one answer to $a^{\frac1b}$, when there are actually $b$ existing roots.

Your math is perfectly fine, I believe it is your calculator that is the issue.

Simply Beautiful Art
  • 74,685
  • I'm running the EXACT same code in a Lua program. (Before the edits) as the arguments to print. – warspyking Dec 17 '15 at 02:00
  • Then it depends if the calculator does $x^a$ or $x^\frac1a$ first. Doing roots second produces more answers. Doing roots second produces less answers. Turning the whole fraction into decimals should give only one answer. – Simply Beautiful Art Dec 17 '15 at 02:04
  • Here's a screenshot: http://postimg.org/image/m68zlwgrt/ (equation, and then the evaluation of each step, then newline) – warspyking Dec 17 '15 at 02:05
  • If a screenshot of the code would help I have that as well: http://postimg.org/image/8ioscemfp/ – warspyking Dec 17 '15 at 02:14
  • I found the problem! Lua was evaluating a^b^c as a^(b^c). I added a set of brackets and good as new. Thanks! – warspyking Dec 17 '15 at 02:19