Simplify. (Assume all variables represent positive real numbers). Leave answer in radical form. \sqrt128a^(6)b^(13)

Question

Simplify. (Assume all variables represent positive real numbers). Leave answer in radical form.


`\sqrt128a^(6)b^(13)`

Answer 1

`\sqrt{128a^(6)b^(13)} = 8 a^(3) b^(6) √(2b)`

Explanation:

Given

`\sqrt{128a^(6)b^(13)}`

Required

Solve

`\sqrt{128a^(6)b^(13)}`

The expression can be split to:

`\sqrt{128a^(6)b^(13)} = √(128) * \sqrt{a^(6)} * \sqrt{b^(13)}`

`\sqrt{128a^(6)b^(13)} = √(64 * 2) * \sqrt{a^(6)} * \sqrt{b^(13)}`

`\sqrt{128a^(6)b^(13)} = √(64) * √(2) * \sqrt{a^(6)} * \sqrt{b^(13)}`

`\sqrt{128a^(6)b^(13)} = √(64) * √(2) * \sqrt{a^(6)} * \sqrt{b^(12 + 1)}`

`\sqrt{128a^(6)b^(13)} = √(64) * √(2) * \sqrt{a^(6)} * \sqrt{b^(12)} * √(b)`

So, we have:

`\sqrt{128a^(6)b^(13)} = 8 * √(2) * a^(6/2) * b^(12/2) * √(b)`

`\sqrt{128a^(6)b^(13)} = 8 * √(2) * a^(3) * b^(6) * √(b)`

Rewrite as:

`\sqrt{128a^(6)b^(13)} = 8 * a^(3) * b^(6)* √(2) * √(b)`

`\sqrt{128a^(6)b^(13)} = 8 a^(3) b^(6)* √(2b)`

`\sqrt{128a^(6)b^(13)} = 8 a^(3) b^(6) √(2b)`