Express each of the following numbers using exponential notation:

$12,500$

Express each of the following numbers using exponential notation:

$27,000$

Express each of the following numbers using exponential notation:

$-343$

Express each of the following numbers using exponential notation:

$62,500$

Compare the following:

$3^4 \mathrm{and} 4^3$

Compare the following:

${\left(-2\right)}^3 \mathrm{and} 1^4$

Compare the following:

$3^5 \mathrm{and} 5^3$

Compare the following:

$2^6 \mathrm{and} 6^2$