To determine: The single radical of the expression: \sqrt[3]{y\sqrt[3]{y\sqrt[3]{y}}}

Jerold

Jerold

Answered question

2021-08-05

To determine: The single radical of the expression
yyy333

Answer & Explanation

ottcomn

ottcomn

Skilled2021-08-06Added 97 answers

Step 1
Formula used:
Product property of radicals:
If a and b are real numbers and n>1 is an integer, the product property is true provided that the radicals are real numbers.
amn=am/n
If m and n are integers and n>1 is an integer, then
amn=am/n
Step 2
Consider the expression yyy333
Rewrite the provided expression as rational exponents.
yyy333=(y(y(y13))13)13
Use the product property and work from inside the parentheses and the expression becomes,
(y(y(y13))13)13=(y(y1+13)13)13
=(y(y43)13)13
=(y y49)13
Add the powers of the same bases.
(y y49)13=(y1+49)13
=(y139)13
=y1327
The obtained expression with rational exponents can be retritten into radicals as.
y1327=(y13)127
=y1327
Therefore, the value of the expression is y1327

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-29Added 2605 answers

Answer is given below (on video)

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