Question

write the expression in simplifed exponetial form and show your work

\[\sqrt{x} * \sqrt[3]{x²}\]

Answer 1

\[\sqrt{x}\times \sqrt[3]{x}=x^{\frac{1}{2}}\times x^{\frac{1}{3}}\] your job is to add the exponents

Answer 2

Actually, it looks like that should be
\[\sqrt{x}*\sqrt[3]{x^2}=x^{\frac{1}{2}}*x^{\frac{2}{3}}\]

Answer 3

so it does

Answer 4

\[\sqrt{x} *\sqrt[3]{x ^{2}}\]
this can be written as
\[x ^{\frac{ 1 }{ 2 }} * x ^{\frac{ 2 }{ 3 }}\]
wchich can be further simplified as
\[x ^{\frac{ 1 }{ 2 } +\frac{ 2 }{ 3 } } = x ^{\frac{ 7 }{ 6 }}\]