Answer:
Option (1) is correct.
On simplifying [tex]14\sqrt[4]{a^5b^2c^4} -7ac\sqrt[4]{ab^2}[/tex] we get, [tex]7ac\sqrt[4]{ab^2}[/tex]
Step-by-step explanation:
Consider the given expression,
[tex]14\sqrt[4]{a^5b^2c^4} -7ac\sqrt[4]{ab^2}[/tex]
We have write the above expression in simplified form.
Consider the first term,
[tex]14\sqrt[4]{a^5b^2c^4}[/tex] can be written as ,
[tex]14\sqrt[4]{a^5b^2c^4}=14\sqrt[4]{a^4ab^2c^4}[/tex]
Taking a and c out the fourth root, we get,
[tex]14\sqrt[4]{a^4ab^2c^4}=14ac\sqrt[4]{ab^2}[/tex]
Now the expression becomes,
[tex]14ac\sqrt[4]{ab^2} -7ac\sqrt[4]{ab^2}[/tex]
Now we can simplify this, taking [tex]7ac\sqrt[4]{ab^2}[/tex] common from both the term, we get,
[tex]7ac\sqrt[4]{ab^2}(2-1)[/tex]
On solving we get,
[tex]\rightarrow 7ac\sqrt[4]{ab^2}[/tex]
Option (1) is correct.
Thus, on simplifying [tex]14\sqrt[4]{a^5b^2c^4} -7ac\sqrt[4]{ab^2}[/tex] we get, [tex]7ac\sqrt[4]{ab^2}[/tex]
