How do you write a^1.5a1.5 in radical form?

1 Answer
Jan 8, 2017

See full explanation below:

Explanation:

Because 1.5 = 3/21.5=32 we can rewrite this expression as:

a^(3/2)a32

We can now use this rule for exponents to modify the expression:

(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))(xa)b=xa×b and x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)xa×b=(xa)b

a^(color(red)(3)/color(blue)(2)) -> a^(color(red)(3) xx 1/color(blue)(2)) -> (a^(color(red)(3)))^(1/color(blue)(2))a32a3×12(a3)12

Now we can use this rule to put this in a radical form:

x^(1/color(red)(n)) = root(color(red)(n))(x)x1n=nx

(a^(color(red)(3)))^(1/color(blue)(2)) -> root(color(blue)(2))(a^(color(red)(3))) -> sqrt(a^(color(red)(3)))(a3)122a3a3