CPM Homework Help : PCT Problem 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 = $(\frac{11}{7})^2$

$5^{4}$
Answer (a):
$\text{Opposite} = -5^4$
$\text{Reciprocal} = -5^4=\frac{1}{5^4}$

$3^{−5}$
Answer (b):
$\text{Opposite} = -3^{-5}$
$\text{Reciprocal} = 3^5$

c. $-11^{−6}$

Answer (c):

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

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

$\frac { 2 } { 7 }$
Answer (d):
$\text{Opposite} = -\frac{2}{7}$
$\text{Reciprocal} =\frac{7}{2}$

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

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