Question

Prime Factorization
35^3 *65*9^13
where do I start?

Answer 1

Ummm I think you want to break down the bases into their prime factorization, then combine powers and such.

So for example the 35 would be..
\[35^3=(5*7)^3=5^3*7^3\]
5 and 7 are prime, so that number is finished, yay!
Can you figure out the primes of 65 and 9? :)

Answer 2

5,13 for 65 3,3 for 9

Answer 3

\[(5^3*7^3)(5^1*13^1)(3^{15}*3^{15})\]
Ok now combine terms with similar bases!
Remember when you multiply terms with similar bases, you ADD the exponents

Answer 4

5*13*5^3*7^3*13^26

Answer 5

how do you use exponents?

Answer 6

\[3^{15}*3^{15}=3^{15+15}=3^{30}\]
When you multiply terms with the same base (3 is our base),
You ADD the exponents, as I have done here.