The basal energy requirement for an individual indicates the minimum number of calories necessary to maintain essential life-sustaining processes such as circulation, regulation of body temperature, and respiration. Given a person's sex, weight $w$ (in kilograms), height $h$ (in centimeters), and age $y$ (in years), we can estimate the basal energy requirement in calories using the following formulas, where $C_f$ and $C_m$ are the calories necessary for females and males, respectively:

$$\begin{aligned} C_f &=66.5+13.8 w+5 h-6.8 y \\ C_m &=655+9.6 w+1.9 h-4.7 y \end{aligned}$$

(a) Determine the basal energy requirements first for a $25$-year-old female weighing $59$ kilograms who is $163$ centimeters tall and then for a $55$-year-old male weighing $75$ kilograms who is $178$ centimeters tall.

(b) Discuss why, in both formulas, the coefficient for $y$ is negative but the other coefficients are positive.

In evaluating negative numbers raised to fractional powers, it may be necessary to evaluate the root and integer power separately. For example, $(-3)^{2 / 5}$ can be evaluated successfully as $\left[(-3)^{1 / 5}\right]^2$ or $\left[(-3)^2\right]^{1 / 5}$, whereas an error message might otherwise appear. Approximate the realnumber expression to four decimal places.

(a) $(-1.2)^{3 / 7} \qquad$ (b) $(-5.08)^{7/3}$

In evaluating negative numbers raised to fractional powers, it may be necessary to evaluate the root and integer power separately. For example, $(-3)^{2 / 5}$ can be evaluated successfully as $\left[(-3)^{1 / 5}\right]^2$ or $\left[(-3)^2\right]^{1 / 5}$, whereas an error message might otherwise appear. Approximate the realnumber expression to four decimal places.

(a) $(-3)^{2 / 5} \qquad$ (b) $(-7)^{4 / 3}$

Evaluate the pair of expressions for $x=1,2,3,4,$ and $5$ by constructing a table of values. Discuss whether or not the two expressions might be equal.

$$\dfrac{113 x^3+280 x^2-150 x}{22 x^3+77 x^2-100 x-350}, \dfrac{3 x}{2 x+7}+\dfrac{4 x^2}{1.1 x^2-5}$$

Replace the symbol $\square$ with either $=$ or $\neq$ to make the resulting statement true, whenever the expression has meaning. Give a reason for your answer.

$$a^{1 / k} ~\square ~ \dfrac{1}{a^k}$$

Simplify the expression.

$$\dfrac{(3 x+2)^{1 / 2}\left(\dfrac{1}{3}\right)(2 x+3)^{-2 / 3}(2)-(2 x+3)^{1 / 3}\left(\dfrac{1}{2}\right)(3 x+2)^{-1 / 2}(3)}{\left[(3 x+2)^{1 / 2}\right]^2}$$

Express the number in the form $a / b$, where $a$ and $b$ are integers.

$$(-0.008) ^{2/3}$$

Express as a polynomial.

$$(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})$$

Simplify the expression, and rationalize the denominator when appropriate.

$$\sqrt[3]{27 x^5 y^3 z^4}$$

Write the expression in the form $a+b i$, where $a$ and $b$ are real numbers.

$$(5-2i)^2$$

If $2 x^2(2x + 3)^4$ is written as a polynomial, what is the leading term?

Replace the symbol $\square$ with either $=$ or $\neq$ to make the resulting statement true, whenever the expression has meaning. Give a reason for your answer.

$$\sqrt[n]{\dfrac{1}{c}} ~\square ~ \dfrac{1}{\sqrt[n]{c}}$$

Solve the equation.

$$\dfrac{5}{2x+3}+\dfrac{4}{2 x-3}=\dfrac{14 x+3}{4 x^2-9}$$

Rewrite the number without using the absolute value symbol, and simplify the result.

(a ) $|-3-4| \qquad$ (b ) $|-5|-|2|\qquad$ (c ) $|7|+|-4|$