Question

Use rational exponents to write x^1/6*y^1/4*z^1/7 as a single radical expression.

Answer 1

really?

Answer 2

i guess the idea here is to add the fractions. to do that you need a common denominator but carefully. denominator is 84 so
\[\frac{1}{6}=\frac{14}{84}\] and
\[x^{\frac{1}{6}}=x^{\frac{14}{84}}=\sqrt[84]{x^{14}}\]

Answer 3

likewise
\[y6{\frac{1}{4}}=\sqrt[84]{y^{21}}\] and
\[z^{\frac{1}{7}}=\sqrt[84]{z^{12}}\]

Answer 4

put it all together to get
\[\sqrt[84]{x^{12}y^{21}z^{12}}\]