Express the following numbers in exponential form with the given base:

$1000$, base $10$

Express the following number in exponential form with the given base:

$512, \text{base} 2$

Express the following numbers in exponential form with the given base:

$243, \text{base} 3$

Find the value of

${13}^2$

Find the value of

$(-7{)}^2$

Find the value of

$(-4{)}^3$

Expand $a^3{b}^2$ and $a^2{b}^3$.

Are they equal?