CPM Homework Help : A2C Problem 10-99

Simplify each expression below. Think about how you could use rules of exponents, the distributive property, and the multiplicative property of one to find shortcuts.

$3^{−2} · 3^{4}$
Answer (a):
$3^{−2} · 3^{4} = 3^{\left(4 − 2\right)} = 9$

$3^{−4} · 3^{4}$
Hint (b):
See part (a).

$\left(3^{−1}+3^{−3}\right) · 3^{4}$
Hint (c):
$3^{4} · 3^{−1} + 3^{4} · 3^{−3}$

$\frac { 3 ^ { - 2 } - 3 ^ { - 1 } } { 3 ^ { - 3 } + 3 ^ { - 4 } }$
Hint (d):
$\frac{3^{4}}{3^{4}}\cdot \frac{3^{-2}-3^{-1}}{3^{-3}+3^{-4}}$
Answer (d):
$-\frac{9}{2}$