Blog: What is t to the negative 4th power

Monday, January 26, 2015

What is t to the negative 4th power

Hello!

By definition, the negative power of something is the inverse of the positive power with the same magnitude:

$\displaystyle{{t}}^{{-{n}}}=\frac{{1}}{{{t}}^{{n}}}.$

This definition is essential because it preserves the properties

$\displaystyle{{a}}^{{n}}\cdot{{a}}^{{m}}={{a}}^{{{n}+{m}}},$ $\displaystyle{{\left({{a}}^{{n}}\right)}}^{{m}}={{a}}^{{{n}\cdot{m}}}$ and $\displaystyle{{\left({a}\cdot{b}\right)}}^{{n}}={{a}}^{{n}}\cdot{{b}}^{{n}}.$

So the answer is: $\displaystyle{{t}}^{{-{4}}}=\frac{{1}}{{{t}}^{{4}}}.$

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Monday, January 26, 2015

What is t to the negative 4th power

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