Question

Simplify the expression and put it into root form:

Answer 1

Answer:  $\sqrt{x^{15}}$

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Explanation:

I'll be using the following rules

• $a^b*a^c = a^{b+c}$ (rule 1)
• $(a^b)^c = a^{b*c}$  (rule 2)
• $a^{b/2} = \sqrt{a^b}$ (rule 3)

So we have these steps:

$\left(x^2*x^{1/2}\right)^3\\\\\left(x^{2+1/2}\right)^3 \ \text{... use rule 1}\\\\\left(x^{4/2+1/2}\right)^3\\\\\left(x^{5/2}\right)^3\\\\x^{(5/2)*3} \ \text{... use rule 2}\\\\x^{15/2}\\\\\sqrt{x^{15}} \ \text{... use rule 3}$