Question #b7a06

Question

1100 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-09T13:33:48

See a solution process below"

Assuming you are looking for the radical form of #4^(2/3)#

We can rewrite the expression as:

#4^(2 xx 1/3)#

We can use this rule for exponents to simplify the expression giving:

#x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#

#4^(color(red)(2) xx color(blue)(1/3)) => (4^color(red)(2))^color(blue)(1/3) => 16^(1/3)#

We can now use this rule for exponents to write the expression in radical form:

#x^(1/color(red)(n)) = root(color(red)(n))(x)#

#16^(1/color(red)(3)) => root(color(red)(3))(16)#

If necessary, we can use this rule for radicals to simplify the expression:

#root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))#

#root(3)(16) => root(3)(color(red)(8) * color(blue)(2)) => root(3)(color(red)(8)) * root(3)(color(blue)(2)) => 2root(3)(2)#

Answer 2 · 2018-01-09T14:01:01

#2root(3)(2)#

#color(blue)(4^(2/3)#

We can simplify this using the law of exponents

#color(brown)(x^(y/z)=root(z)(x^y)#

So,

#rarr4^(2/3)=root(3)(4^2)#

#color(green)(rArrroot(3)(16)##= ##color (red)(root (3)(2×2^3)#
#color (blue)(2root (3)(2))#
Hope this helps!!! ☺☻