Question

Simplify radical sign 16a^8b^-2

Answer 1

Answer:

$\frac{ {4a}^{4} }{b}$

solution,

$\sqrt{16 {a}^{8} {b}^{ - 2} }$

Use negative power rule:

${x}^{ - a} = \frac{1}{ {x}^{a} }$

$\sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } }$

Simplify:

$\sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } }$

Use this rule:

$\sqrt{ab} = \sqrt{a} . \sqrt{b}$

$\frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } }$

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...