Question

Francisco and Ryan are stuck simplifying radical expressions. Francisco has simplified to the quantity of x to the one half power, over x to the three eighteenth power. Ryan has simplified to the twenty seventh root of the quantity of x to the second times x to the third times x to the fourth. Using full sentences, describe how to fully simplify Francisco and Ryan's expressions. Describe if Francisco and Ryan started with equivalent expressions or if they started with expressions that are not equal.

Answer 1

than i understand it correct

Francisco has \[\frac{x ^{1/2} }{x ^{3/18} } = ?\]

Ryan has \[\sqrt[27]{x^{2}*x^{3}*x^{4}} = ?\]

these above wrote are correct ?

Answer 2

suppose yes so in case of the first one when you have the same base on different power divided what you need to do with exponents ?

and in the case second one when you multiplie the same base with different exponent what you need to do with exponents ?
and a little help here - one example how can you rewrite the square root in exponential form

\[\sqrt[2]{x} = x^{1/2}\]

so how you see on this example the denominator of fractional exponent is the index of the radical

hope helped understandably easy