Answer: [tex]\sqrt{x^{15}}[/tex]
=====================================================
Explanation:
I'll be using the following rules
- [tex]a^b*a^c = a^{b+c}[/tex] (rule 1)
- [tex](a^b)^c = a^{b*c}[/tex] (rule 2)
- [tex]a^{b/2} = \sqrt{a^b}[/tex] (rule 3)
So we have these steps:
[tex]\left(x^2*x^{1/2}\right)^3\\\\\left(x^{2+1/2}\right)^3 \ \text{... use rule 1}\\\\\left(x^{4/2+1/2}\right)^3\\\\\left(x^{5/2}\right)^3\\\\x^{(5/2)*3} \ \text{... use rule 2}\\\\x^{15/2}\\\\\sqrt{x^{15}} \ \text{... use rule 3}\\\\[/tex]
