Question

Which expression is equivalent to ^3 square root 64a^6 b^7 c^9

Answer 1

`\sqrt[3]{64a^6b^7c^9}\Rightarrow 4a^2b^2c^3\sqrt[3]{b}`.

Option 2 is correct.

Explanation:

Given:
`\sqrt[3]{64a^6b^7c^9}`

We need to simplify the complex radical and to compare with given options which is equivalent to this.

`\Rightarrow \sqrt[3]{64a^6b^7c^9}`

separate the radical 3 with each term inside the radical.

`\Rightarrow \sqrt[3]{64}\cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^7}\cdot \sqrt[3]{c^9}`

Simplify each radical

`\Rightarrow 4\cdot a^2\cdot b^2\sqrt[3]{b}\cdot c^3`

Write all term together

`\Rightarrow 4a^2b^2c^3\sqrt[3]{b}`

Hence, The equivalent expression
`\Rightarrow 4a^2b^2c^3\sqrt[3]{b}`

Answer 2

`4a^(2) b^(2) c^(3) (\sqrt[3]{b})`

Explanation:

The given expression is :

`\sqrt[3]{(64}a^(6)b^(7) c^(9) )`

Writing 64 ,a,b,c as cubes we have:

=
`\sqrt[3]{(}4^(3)( a^(2))^3( b^(2))^3.b( c^(3) )^3)`

Using radical rule we have :

=
`4a^(2) b^(2) c^(3) (\sqrt[3]{b})`.

The second option is the right answer.