How do you simplify $(\root [ 11] { 9x ^ { 6} y } ) ^ { 7}$ ?

Question

1420 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-20T03:25:02

$" "$
$color(brown)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}= [9^(7/11)][x^(42/11)][y^(7/11)]$

$" "$
We have $color(red)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}$

Useful Exponent formula:

$color(blue)((a^m)^n = a^(mn)$

$color(blue)(root(n)m = m^(1/n)$

$color(blue)(root(n)(a^m) = a^(m/n)$

Consider:

$(\root [ 11] { 9x ^ { 6} y } ) ^ { 7}$ given expression

Simplify this expression using the formula list above.

$[root(11)(9)*root(11)(x^6)*root(11)(y)]^7$

$rArr [root(11)(9^1)*root(11)(x^6)*root(11)(y^1)]^7$

$rArr [9^(1/11)*x^(6/11)*y^(1/11)]^7$

$rArr 9^(7/11)*x^(42/11)*y^(7/11)$

Hence,

$color(brown)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}= [9^(7/11)][x^(42/11)][y^(7/11)]$

Hope it helps.

How do you simplify (\root [ 11] { 9x ^ { 6} y } ) ^ { 7}(\root [ 11] { 9x ^ { 6} y } ) ^ { 7}?