  ### Home > CCAA > Chapter 9 Unit 8 > Lesson CC2: 9.2.2 > Problem9-69

9-69.

Simplify each of the following expressions.

1. $3\frac{1}{5}\cdot\frac{7}{4}$

Convert the mixed number into a fraction greater than one.

$\frac{16}{5}\left(\frac{7}{4}\right)$

$\frac{28}{5}=5\frac{3}{5}$

1. $5 ^ { 3 } \cdot ( - \frac { 4 } { 5 } )$

$- \frac{4}{5} = (-1)(4)\left(\frac{1}{5}\right)$

Notice that the $5$ in the denominator is like dividing by $5$.

$\frac{5^{\left(3\right)}}{5\left(-4\right)}$

$5^2(-4)=-100$

1. $2 ^ { 4 } \cdot \frac { 5 } { 8 }$

This can be rewritten as:

$2^{4}\left(\frac{5}{2^{3}}\right)$

See part (b).

$10$

1. $- \frac { 1 } { 2 } \cdot 3 ^ { 2 }$

Use the order of operations.

1. $- \frac { 5 } { 6 } + ( \frac { 1 } { 2 } ) ^ { 2 }$

Use the order of operations.

$-\frac{5}{6}+\frac{1}{4}$

$-\frac{20}{24}+\frac{6}{24}=-\frac{14}{24}$

1. $( - \frac { 4 } { 5 } ) ^ { 2 } - \frac { 3 } { 50 }$

Notice that squaring a negative number has the same result as multiplying two negative numbers: the product is always positive.

1. $\left(\frac{3}{10}\right)^2-\left(-\frac{2}{5}\right)^2$

1. $8^2\left(-\frac{7}{8}\right)-\frac{1}{2}$
$8^{(2-1)}(-7)-\frac{1}{2}$
$8(-7)-\frac{1}{2}$
$(-56)-\frac{1}{2}$
$-56\frac{1}{2}$