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

9-132.

Simplify each of the following expressions. Homework Help ✎

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

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

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