### Home > ACC7 > Chapter 8 Unit 9 > Lesson CC3: 8.2.2 > Problem8-66

8-66.

Simplify each expression.

1. $\frac { 3 ^ { 2 } \cdot 5 ^ { 3 } \cdot 8 } { 3 \cdot 5 ^ { 3 } \cdot 8 }$

Recall that when you divide a number by itself, the quotient is $1$. Can you find any factors that are in both the numerator and the denominator?

You can rewrite the expression.

$\frac{3\cdot3\cdot5\cdot5\cdot5\cdot8}{3\cdot5\cdot5\cdot5\cdot8}$

There are three $5$'s on the top and on the bottom, which may be removed by division. Similarly, there are $8$'s and $3$'s that can be removed.

$3$

2. $\left(3x\right)^{4}$

Rewrite the expression and simplify.
$\left(3x\right)\left(3x\right)\left(3x\right)\left(3x\right)$

$81x^{4}$

3. $3 ^ { 3 } \cdot 3 ^ { 5 } \cdot ( \frac { 1 } { 3 } ) ^ { 2 }$

You can rewrite this expression as:

$\frac{3^{3}3^{5}}{3^{2}}$

4. $\frac { 7 ^ { 4 } \cdot 9 ^ { 2 } } { 9 ^ { 3 } \cdot 7 ^ { 2 } }$

See (a).