Question

Which is equal to 9^1/3 * 9^1/6

Answer 1

Do you want an answer or explanation?

Answer 2

both

Answer 3

Mk,

Do you know exponential rules?

Basically \(\ \sf x^{\frac{1}{2}} \implies \sqrt{x} \)

Therefore, \(\ \sf 9^{\frac{1}{3}} \implies \sqrt[3]{9} \) Applying it to both terms you get:

\(\ \sf \sqrt[3]{9} \times \sqrt[6]{9}\)

Can you simplify this?

Answer 4

343.65?

Answer 5

In short yes, you can.

The squareroot of 9 is 3^2. Therefore, \( \sf \sqrt[3]{3^2} \times \sqrt[6]{3^2} \)

Now undoing the rule we applied, we result with \( \sf 3^{\frac{2}{3}} \times 3^{\frac{2}{6}} \)

After simplfying you get 3^2/3 * 3^2/6 ==> 2/6 = 1/3

3^2/3 * 3^1/3; bases are the same, so add the exponents: 2/3 + 1/3 = 3/3 = 1

So 3^1 = 3. Your final answer is 3.

Answer 6

I have to go. Tag me if you need further help later on :)