Question

what is the expression in radical form? (3p^3q)^(3/4)

1. sqrt3{3p^{12}q^{4}}
2. sqrt4{3p^{9}q^{3}}
3. sqrt4{27p^{9}q^{3}}
4. sqrt3{81p^{12}q^{4}}

Explanation:

Step1: Apply power - of - a - product rule

$(3p^{3}q)^{\frac{3}{4}}=3^{\frac{3}{4}}(p^{3})^{\frac{3}{4}}q^{\frac{3}{4}}$

Step2: Apply power - of - a - power rule

$(p^{3})^{\frac{3}{4}} = p^{3\times\frac{3}{4}}=p^{\frac{9}{4}}$, and $3^{\frac{3}{4}}=\sqrt[4]{3^{3}}=\sqrt[4]{27}$

Step3: Write in radical form

$3^{\frac{3}{4}}(p^{3})^{\frac{3}{4}}q^{\frac{3}{4}}=\sqrt[4]{27p^{9}q^{3}}$

Answer:

$\sqrt[4]{27p^{9}q^{3}}$ (corresponding to the third option in the multiple - choice list)