Question

Simplify radical sign 16a^8b^-2

Answer 1

`\frac{ {4a}^(4) }{b}`

solution,

`\sqrt{16 {a}^(8) {b}^( - 2) } \\`

Use negative power rule:

`{x}^( - a) = \frac{1}{ {x}^(a) }`

`\sqrt{ {16}^(8) * \frac{1}{ {b}^(2) } } \\`

Simplify:

`\sqrt{ \frac{ {16a}^(8) }{ {b}^(2) } } \\ = \frac{ \sqrt{ {16a}^(8) } }{ \sqrt{ {b}^(2) } } \\`

Use this rule:

`√(ab) = √(a) . √(b)`

`\frac{ \sqrt{16. \sqrt{ {a}^(8) } } }{ \sqrt{ {b}^(2) } }`

Since, 4*4=16 ,the square root of 16 is 4

`\frac{ \sqrt{ {4}^(2) } \sqrt{ {a}^(8) } }{ \sqrt{ {b}^(2) } } \\ = \frac{4 \sqrt{ {a}^(8) } }{ \sqrt{ {b}^(2) } }`

Simplify:

`\frac{4 \: \sqrt{ {(a}^{4) ^(2) } } }{ \sqrt{ {b}^(2) } } \\ = \frac{4 {a}^(4) }{b}`

Hope this helps...

Good luck on your assignment...