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

Francisco has simplified to the quantity of x to the one half power, over x to the three eighteenth power.
(x^1/2) / (x^3/18)
x^(1/2-3/18)
x^1/3

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.
²⁷√x²x³x⁴
²⁷√x⁹
(x)^9/27
x^1/3

Answer 2

Answer:

Both Ryan and Fransisco started off with equivalent expressions. this expression was x^ 1/3.

Step-by-step explanation:

Fransisco simplified (x^ 1/2) / (x^ 3/18).  

He ended up with x^ 1/3 (x to the 1/3 power) by doing (x^1/2) / (x^3/18) by subtracting the powers x^(1/2 - 3/18). x^(1/2 - 3/18) can be converted to x^(9/18 - 3/18) to get the denominators the same. Then subtract to get x^ 6/18 which simplifies to x^ 1/3.  

Ryan simplified 27√ x^2 . x^3 . x^4.  

Step one is to combine the powers. Since all of the variables inside of the radical are the same, they can be combined into one term by adding the exponents. This makes the equation 27√x^9. In order to put it into the correct form, you must make the 27 the denominator and 9 the numerator in the exponent. This makes the expression x^ (9/27), which can be simplified to x^ 1/3.  

Both Ryan and Fransisco started off with equivalent expressions. this expression was x^ 1/3.