# The power of a power

My teacher gets the following: $(x^{2})^{12-k} = x^{2k-24}$

Where I get the following: $(x^{2})^{12-k} = x^{24-2k}$

I'd like to think of $2(12-k)$ as $2*12 - 2*k$ or $-2k + 24$. Why/how am I wrong?

He did the following: $x^{4k} * {a^{12-k} \over (x^{2})^{12-k}} = x^{4k} * a^{12-k} * x^{2k-24}$

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Note: $(a^b)^c = a^{bc}$. But without parenthesis, $a^{b^c}$ means $a^{(b^c)}$. Which one are you talking about, and what is the context? – Arturo Magidin Feb 13 '12 at 4:02
You and your teacher are both wrong, which probably means that you have not accurately reported what your teacher actually did. – Gerry Myerson Feb 13 '12 at 4:04
Sorry, clarified. – Hum Feb 13 '12 at 4:05
No, not clarified: corrected. If you are now accurately reporting what your teacher got, your teacher made a mistake. – Gerry Myerson Feb 13 '12 at 4:08
@GerryMyerson I think you're being a little unpleasant. I think it is quite logical to expect him to be learning $$(a^b)^c = a^{bc}$$. – Pedro Tamaroff Feb 13 '12 at 4:18

In that case, what the teacher is doing is $$\frac1{(x^2)^{12-k}}=(x^2)^{k-12}=x^{2k-24}$$