How do you simplify -root8(4)+5root8(4)?

1 Answer
Jun 12, 2017

See a solution process below:

Explanation:

First, rewrite this expression as:

-1root(8)(4) + 5root(8)(4)

Next, factor and combine these like terms:

(-1 + 5)root(8)(4) = 4root(8)(4)

We can now rewrite this expression using this rule for exponents and radicals:

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

4root(color(red)(8))(4) = 4 * 4^(1/color(red)(8))

We can now use these two rules of exponents to again rewrite this expression:

a = a^color(red)(1) and x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))

4 * 4^(1/8) => 4^color(red)(1) xx 4^color(blue)(1/8) = 4^(color(red)(1) + color(blue)(1/8)) = 4^(color(red)(8/8) + color(blue)(1/8)) = 4^(9/8)

Or, depending on the solution you are looking for, using the reverse of the rule above:

4^(9/8) = 4^(9 * 1/8) = (4^9)^(1/8) => root(8)(4^9)

Some of the simplifications are, depending on what you are working on:

4root(8)(4) or 4^(9/8) or root(8)(4^9)