How do you simplify ${(81 a^{8} b^{4})}^{\frac{1}{4}}$ $(81a^8 b^4)^(1/4)$ ?

Question

2426 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-20T19:52:54

${(81 a^{8} b^{4})}^{\frac{1}{4}} = 3 a^{2} | b |$ $(81a^8b^4)^(1/4) = 3a^2abs(b)$

${(81 a^{8} b^{4})}^{\frac{1}{4}}$ $(81a^8b^4)^(1/4)$

$= {(3^{4} {(a^{2})}^{4} b^{4})}^{\frac{1}{4}}$ $=(3^4(a^2)^4b^4)^(1/4)$

$= {(3^{4} {(a^{2})}^{4} {| b |}^{4})}^{\frac{1}{4}}$ $=(3^4(a^2)^4abs(b)^4)^(1/4)$

$= {({(3 a^{2} | b |)}^{4})}^{\frac{1}{4}}$ $=((3a^2abs(b))^4)^(1/4)$

Now $3 a^{2} | b | \geq 0$ $3a^2abs(b) >= 0$ , so

$= {(3 a^{2} | b |)}^{4 \cdot \frac{1}{4}}$ $=(3a^2abs(b))^(4 * 1/4)$

$= {(3 a^{2} | b |)}^{1}$ $=(3a^2abs(b))^1$

$= 3 a^{2} | b |$ $=3a^2abs(b)$

How do you simplify (81a8b4)14(81a^8 b^4)^(1/4)?