Question

How do I evaluate (1/9)^3

Answer 1

`3^(-6)` or 1/729

Explanation:

First recognize that 1/9 is equal to 3^-2

This is because when we add a negative exponent to a number we start to express its exponents as a fraction of 1.

Let me further explain

6^1 = 6

6^2 = 36

So... using this logic

6^-1 = 1/6

6^-2 = 1/36

So for this problem..

1/9 = 3^-2

Then we have a power to a power which when you have a power raised to a power, you multiply

So.. (3^-2)^3 = 3 which is the base to the power of -2 x 3 which is -6

So the answer is 3^-6

Which equals 1/3^6 power which is 1/729.