Write problem as a single radical using the smallest possible root. 16

Question

asked Dec 12, 2023 92.2k views

1 Answer

Bobby · Answer 1 · 2023-12-18T17:12:10+0000

The radical expression is given to be:

$√(n^5)\sqrt[3]{n^4}$

Recall the rule:

$\sqrt[n]{x}=x^{(1)/(n)}$

Therefore, the expression becomes:

$√(n^5)\sqrt[3]{n^4}=n^{(5)/(2)}\cdot n^{(4)/(3)}$

Recall the rule:

$x^a\cdot x^b=x^(a+b)$

Therefore, we have:

$n^5\cdot n^{(4)/(3)}=n^{(5)/(2)+(4)/(3)}$

Since:

Therefore, the expression becomes:

$n^{(5)/(2)+(4)/(3)}=n^{(23)/(6)}$

Therefore, we can rewrite the radical to be:

$\Rightarrow\sqrt[6]{n^(23)}$