How do I figure the equal factors of 9 to the ninth power?

Answer 1

This is easier than it may seem.

9^9 is the same as 9 multiplied by itself 9 times:

9^9 = 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9

Now, you also know that
9 = 3 x 3 (at least I hope so, lol!)

So, substitute (3x3) for each '9' in the first equation

9^9 = (3x3) x (3x3) x (3x3) x (3x3) x (3x3) x (3x3) x (3x3) x (3x3) x (3x3)

9^9 = 3^18

There is an easier way to do this problem though, using the 9 = 3x3 substitution directly in the original equation.

9^9 = (3x3)^9 = (3^2)^9 = (3^9) x (3^9)

3^9 = 19683

9^9 = (3^9) x (3^9) = 19683 x 19683 = 387,420,489


Could also calculate 9^9 and then take the square root of the result to get the equal factors.

Hope this helps,

-Guru

Answer 2

Hmm... not exactly sure of your question.

9 to the 9th power (often written 9^9) is the same as:

9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9

If you factor this further it is:
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3

(3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3) x (3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3)

This is the same as:
3^9 x 3^9 = 19683 x 19683

You could also group this as:
(3 x 3 x 3 x 3 x 3 x 3) x (3 x 3 x 3 x 3 x 3 x 3) x (3 x 3 x 3 x 3 x 3 x 3)
3^6 x 3^6 x 3^6 = 729 x 729 x 729

Also:
(3 x 3 x 3) x (3 x 3 x 3) x (3 x 3 x 3) x (3 x 3 x 3) x (3 x 3 x 3) x (3 x 3 x 3)
3^3 x 3^3 x 3^3 x 3^3 x 3^3 x 3^3 x 3^3 = 27 x 27 x 27 x 27 x 27 x 27

There is also 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 that we had at the beginning, and the 3 x 3 x 3 x ... x 3 x 3 x 3 from above.

Is that what you meant by "equal factors"?

Answer 3

Use the laws of exponent that says you multiply the exponents when you have the power of a power. So

9^9 = (3^2)^9 Now multiply the exponents 2 x 9 = 18 so

9^9 = 3^18 so there are 18 equal factors of 3.

Answer 4

Hi,

9^9 = (3^2)^9 = 3^18

3^18 would have 2 equal factors of 3^9 or 19,683.

So (19,683)(19,683) = 9^9

I hope that helps!! :-)