### Home > PC > Chapter 1 > Lesson 1.1.4 > Problem1-54

1-54.

Give the opposite and reciprocal of each expression without doing any arithmetic. If the given expression involves fractions, give the answer with positive exponents.

Example: $3^{2}$

Solution: $\text{Opposite} = −3^{2}$

$\text{Reciprocal} = 3^{−2}$ or $\frac { 1 } { 3 ^ { 2 } }$

Example:$( \frac { 7 } { 11 } ) ^ { 2 }$

Solution: Opposite = $-(\frac{7}{11})^2$

Reciprocal =$(\frac{11}{7})^2$

1. $5^{4}$

$\text{Opposite} = -5^4$

$\text{Reciprocal} = -5^4=\frac{1}{5^4}$

1. $3^{−5}$

$\text{Opposite} = -3^{-5}$

$\text{Reciprocal} = 3^5$

c.$-11^{−6}$

$\text{Opposite} = 11^{-6}$

$\text{Reciprocal} = -11^6$

1. $\frac { 2 } { 7 }$

$\text{Opposite} = -\frac{2}{7}$

$\text{Reciprocal} =\frac{7}{2}$

1. $( \frac { 11 } { 9 } ) ^ { 2 }$

$\text{Opposite} = -\left(\frac{11}{9}\right)^2$

$\text{Reciprocal} = \left(\frac{11}{9}\right)^{-2}= \left(\frac{9}{11}\right)^{2}$

1. $( \frac { 7 } { 13 } ) ^ { - 5 }$

$\text{Opposite} = -\left(\frac{7}{13}\right)^{-5}$

$=\left(-\frac{7}{13}\right)^{-5}$

$\text{Reciprocal} = \left(\frac{7}{13}\right)^{5}$