How do I simplify $(t^{3}) (t^{n - 3})$ $(t^3)(t^(n-3))$ ?

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How do I simplify $(t^{3}) (t^{n - 3})$ $(t^3)(t^(n-3))$ ?

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Answer 1 · 2015-07-26T18:12:41

$(t^{3}) (t^{n - 3}) = t^{3 + (n - 3)} = t^{n}$ $(t^3)(t^(n-3)) = t^(3+(n-3)) = t^n$

with some restrictions...

Explanation:

With certain restrictions, $a^{b} \cdot a^{c} = a^{b + c}$ $a^b*a^c = a^(b+c)$

If $t = 0$ $t = 0$ then we require $n - 3 > 0$ $n-3 > 0$ , that is $n > 3$ $n > 3$ , in order that $t^{n - 3}$ $t^(n-3)$ be defined.

If $t < 0$ $t < 0$ then both the left and right sides of the equation are only defined if $n in ZZ$ , but perhaps the variable name $n$ is supposed to imply that anyway.

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How do I simplify $(t^{3}) (t^{n - 3})$ $(t^3)(t^(n-3))$ ?

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How do I simplify $(t^{3}) (t^{n - 3})$ $(t^3)(t^(n-3))$ ?