Question

How do I solve 1/9 to the -3 power= 9 to the ____power

Answer 1

Your answer is 9 to the 3 power, where the blank is 3.

To find this, I first wrote out the equation:

`{ ( (1)/(9))}^( - 3) = {9}^(x)`

Then I found the value of (1/9)^-3, which you can do by first flipping the fraction 1/9 as the power is negative, to get 9/1, or just 9, and then putting 9 to the power of 3 to get 27.

You could have already noticed that we got 9³ = 9^x, so x = 3, but if you didn't then you would just need to see that 27 is 9³.

I hope this helps!

Answer 2

When you have a fraction with a negative power, change the power number into positive, and then flip the fraction into a whole number (or if it started as a whole number, flip to fraction).

1/9^-3 = 9^3

3 is your answer, or "9 to the 3rd power"

hope this helps