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Art [367]
3 years ago
7

Simplify radical sign 16a^8b^-2

Mathematics
1 answer:
almond37 [142]3 years ago
6 0

Answer:

<h2>\frac{ {4a}^{4} }{b}</h2>

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...

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