  ### Home > CC3 > Chapter 9 > Lesson 9.2.5 > Problem9-132

9-132.

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 would have an exponent of $-1$.

$5^{(3-1)}(-4)$

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

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. $-\frac{1}{2}\cdot3^2$

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

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