How do you multiply \root[ 5] { 2} \cdot \root [ 3] { 5} \cdot \root [ 6] { 4}?

1 Answer
Jun 15, 2017

2^(8/15) xx 5^(1/3)

Explanation:

First, rewrite the problem using exponents:

2^(1/5) xx 5^(1/3) xx 4^(1/6)

4 is simply 2^2:

2^(1/5) xx 5^(1/3) xx 2^(2/6)

Now we have two numbers with base 2. We are allowed to add those exponents together:

2^(1/5+2/6) xx 5^(1/3)

Let's focus on the exponent for 2 for now:

1/5+2/6

Simplify 2/6

1/5+1/3

Now use common denominators. Multiply 1/5 by 3/3 and 1/3 by 5/5:

1/5(3/3)+1/3(5/5)

This becomes:

3/15+5/15

Add the numerators together:

8/15

So our solution is:

2^(8/15) xx 5^(1/3)