How do you simplify #root3(192x^9)#?

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Answer 1 · 2015-09-11T09:53:19

#root3(192x^9) = color(green)(4 * x^3 *root3(3)#

In exponents, #color(blue)(rootn(a*b) = rootna*rootnb#

Hence #root3(192x^9) = root3(192)*root3(x^9)#---------(1)

Let's find #root3(192)# first

# = root3(2^6 * 3)#

# = root3(2^6)*root3(3)#

In exponents, #color(blue)(rootn(a^b) = a^(b/n)#

Hence #root3(2^6)*root3(3) = 2^(6/3) *root3(3)#

#= 2^2 *root3(3)#

#= 4 *root3(3)#

Now let's find #root3(x^9)#

#= x^(9/3)#

# = x^3#

Plugging the two values into (1), we get

#root3(192x^9) = 4 *root3(3)*x^3#

#root3(192x^9) = color(green)(4 * x^3 *root3(3)#