Example: Compare $2^8$ and $8^2$.
Solution:
$2^8 = 256$
When comparing numbers in scientific notation, express them with the same power of 10.
Example: Compare $2.7 \times 10^{12}$ and $1.5 \times 10^8$.
Solution:
Let $a = 2.7 \times 10^{12}$ and $b = 1.5 \times 10^8$.
We can rewrite $a$:
Since $27000$ is greater than $1.5$, we conclude that:
Example: Express $432$ as a product of powers of prime factors.
Solution:
Prime numbers are $2, 3, 5, 7, 11…$.
Using the division method (see diagram above):
In power notation: