> [!NOTE] Lemma > For all $x>0,$ $p,q\in \mathbb{R},$ $x^{p+q}=x^{p}x^{q}$where $x^{p}$ denotes the $p$th [[Real Power of Real Number|power]] of $x.$ **Proof**: By definition and [[Real Exponential Function of Sum]], $x^{p}x^{q}= \exp(p\log(x))\exp (q\log(x))=\exp((p+q)\log(x))=x^{p+q}.$