Math Help - Exact Value of Indices

1. Exact Value of Indices

Is there a simple way to find the exact value of these? There are no examples in the textbook for indices, other than powers of 1/2 and 1/3.

1. (1/36)^-3/2
2. 216^1/6 x 216^1/6
3. 9^3/2 x 7^1

Is there a simple way to find the exact value of these? There are no examples in the textbook for indices, other than powers of 1/2 and 1/3.

1. (1/36)^-3/2
2. 216^1/6 x 216^1/6
3. 9^3/2 x 7^1

$\left(\frac{1}{36}\right)^{-\frac{3}{2}} = 36^{\frac{3}{2}} = \left(36^{\frac{1}{2}}\right)^3 = 6^3 = 216$

$\left(216^{\frac{1}{6}}\right)^2 = 216^{\frac{1}{3}} = 6$

you do the last one ...

3. hi
$\forall x\in \mathbb{R}^{+*},x^{\frac{1}{n}}=\exp(\frac{1}{n}\l n x)$

4. 9^3/2 x 7^1
= (9^1/2)^3 x 7
= 27 x 7
= 189.

9^3/2 x 7^1
= (9^1/2)^3 x 7
= 27 x 7
= 189.
Good