Question

What is the simplified form of the following expression? Assume a>0 and c>0 14(4√a5b2c4)-7ac(4√ab2)

Answer 1

14(4√a5b2c4)-7ac(4√ab2)

= 14ac(4√ab2) - 7ac(4√ab2)

= 7ac(4√ab2)

answer is A. first choice

Answer 2

we have

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

we know that

`\sqrt[4]{a^(5)}=a \sqrt[4]{a}`

`\sqrt[4]{c^(4)}=c`

substitute

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

therefore

the answer is

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