Answer
Part A:
$a^{2}b^{2}$
Part B:
$3a^{3}b^{2}$
Work Step by Step
Note: $a^{n}a^{m} = a^{n + m}$
Note: $\frac{a^{n}}{a^{m}}$ = $a^{n-m}$
Note: $a^{0} = 1$
Part A:
The problem can be rewritten as:
$\frac{a^{2}b^{0}}{b^{-2}}$ since $b^{0} = 1$
To eliminate the negative exponent the b components can be simplified:
$\frac{b^{0}}{b^{-2}}$ = $b^{0 - (-2)}$ = $b^{2}$
Therefore, the problem simplifies to:
$a^{2}b^{2}$
Part B:
Using the first note:
$(a^{2}b^{4})(3ab^{-2})$ = $3a^{2 + 1}b^{4 + (-2)}$ = $3a^{3}b^{2}$
