### Home > A2C > Chapter 10 > Lesson 10.2.3 > Problem10-99

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.

1. $3^{−2} · 3^{4}$

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

1. $3^{−4} · 3^{4}$

See part (a).

1. $\left(3^{−1}+3^{−3}\right) · 3^{4}$

$3^{4} · 3^{−1} + 3^{4} · 3^{−3}$

1. $\frac { 3 ^ { - 2 } - 3 ^ { - 1 } } { 3 ^ { - 3 } + 3 ^ { - 4 } }$

$\frac{3^{4}}{3^{4}}\cdot \frac{3^{-2}-3^{-1}}{3^{-3}+3^{-4}}$

$-\frac{9}{2}$