Manipulating powers

2^1/5 x 4^2/5 = ?

Phil

Student grade 11

Hi Phil,

One of the rules of exponents tell you how to multiply two powers with the same base. That is

3^2/3 x 3^4/3 = 3^{2/3 + 4/3} = 3^6/3 = 3²

In your problem you can write the two powers with the same base since 4 = 2². Thus

2^1/5 x 4^2/5 = 2^1/5 x (2²)^2/5 = 2^1/5 x 2^4/5

Now you can complete the problem.

Cheers,
Penny Go to Math Central