Question

simplify the following number.
$(-8)^{7/3}$
$(-8)^{7/3}=\square$

Explanation:

Step1: Recall exponent rule \(a^{m/n}=\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\)

We can rewrite \((-8)^{7/3}\) as \(((-8)^{1/3})^7\) or \((-8)^{7\times\frac{1}{3}}\). First, find \((-8)^{1/3}\). Since \((-2)^3 = -8\), so \(\sqrt[3]{-8}=-2\).

Step2: Raise the result to the 7th power

Now we have \((-2)^7\). Calculate \((-2)^7\): \((-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)= -128\).

Answer:

\(-128\)