### Home > MC2 > Chapter 10 > Lesson 10.2.3 > Problem10-111

10-111.

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

Refer to the Math Notes box of Lesson 10.1.6.

Notice that the 5 in the denominator would have an exponent of 1.

5(3 − 1)(−4)

52(−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. $8 ^ { 2 } ( - \frac { 7 } { 8 } ) - \frac { 1 } { 2 }$
$8^{(2-1)}(-7)-\frac{1}{2}$
$8(-7)-\frac{1}{2}$
$(-56)-\frac{1}{2}$
$-56\frac{1}{2}$