Question

What is the simplified form of the following expression?Assume a is greater/= 0, and c is greater/= 0

14(^4√a^5 b^2 c^4) -7ac(^4√ab^2)

A) 7ac(^4√ab^2)

B) 7(^4√ab^2)

C) -7(^4√ab^2)

D) -7ab(^4√ab^2)

Answer 1

Option (1) is correct.

On simplifying
`14\sqrt[4]{a^5b^2c^4} -7ac\sqrt[4]{ab^2}` we get,
`7ac\sqrt[4]{ab^2}`

Explanation:

Consider the given expression,

`14\sqrt[4]{a^5b^2c^4} -7ac\sqrt[4]{ab^2}`

We have write the above expression in simplified form.

Consider the first term,

`14\sqrt[4]{a^5b^2c^4}` can be written as ,

`14\sqrt[4]{a^5b^2c^4}=14\sqrt[4]{a^4ab^2c^4}`

Taking a and c out the fourth root, we get,

`14\sqrt[4]{a^4ab^2c^4}=14ac\sqrt[4]{ab^2}`

Now the expression becomes,

`14ac\sqrt[4]{ab^2} -7ac\sqrt[4]{ab^2}`

Now we can simplify this, taking
`7ac\sqrt[4]{ab^2}` common from both the term, we get,

`7ac\sqrt[4]{ab^2}(2-1)`

On solving we get,

`\rightarrow 7ac\sqrt[4]{ab^2}`

Option (1) is correct.

Thus, on simplifying
`14\sqrt[4]{a^5b^2c^4} -7ac\sqrt[4]{ab^2}` we get,
`7ac\sqrt[4]{ab^2}`