Chapter 10

Write each expression in the form \(a+b i .\) $$ 7-\sqrt{-25} $$

Simplify each exponential expression. $$ \left(-2 x^{3} y^{2}\right)^{5} $$

Basal metabolic rate \((B M R)\) is the number of calories per day a person needs to maintain life. A person's basal metabolic rate \(B(w)\) in calories per day can be estimated with the function \(B(w)=70 w^{3 / 4},\) where \(w\) is the person's weight in kilograms. Use this information to answer Exercises 95 and \(96 .\) Estimate the BMR for a person who weighs 60 kilograms. Round to the nearest calorie. (Note: 60 kilograms is approximately 132 pounds.)

Find the midpoint of each line segment whose endpoints are given. \((\sqrt{2}, 3 \sqrt{5}) ;(\sqrt{2},-2 \sqrt{5})\)

Write each expression in the form \(a+b i .\) $$ 5-\sqrt{-16} $$

Simplify each exponential expression. $$ \left(4 y^{6} z^{7}\right)^{3} $$

Basal metabolic rate \((B M R)\) is the number of calories per day a person needs to maintain life. A person's basal metabolic rate \(B(w)\) in calories per day can be estimated with the function \(B(w)=70 w^{3 / 4},\) where \(w\) is the person's weight in kilograms. Use this information to answer Exercises 95 and \(96 .\) Estimate the BMR for a person who weighs 90 kilograms. Round to the nearest calorie. (Note: 90 kilograms is approximately 198 pounds.)

Find the midpoint of each line segment whose endpoints are given. \((\sqrt{8},-\sqrt{12}) ;(3 \sqrt{2}, 7 \sqrt{3})\)

Write each expression in the form \(a+b i .\) $$ \frac{6+\sqrt{-18}}{3} $$

Simplify each exponential expression. $$ \left(-3 x^{2} y^{3} z^{5}\right)\left(20 x^{5} y^{7}\right) $$

The number of cellular telephone subscribers in the United States from 1995 through 2009 can be modeled by \(f(x)=17 x^{16 / 15},\) where y is the number of cellular telephone subscriptions in millions, \(x\) years after \(1995 .\) (Source: Based on data from CTIA-The Wireless Association, 1995-2009) Use this information to answer Exercises 97 and 98. Use this model to estimate the number of cellular subscriptions in \(2009 .\) Round to the nearest tenth of a million.

Find the midpoint of each line segment whose endpoints are given. (4.6,-3.5)\(;(7.8,-9.8)\)

Write each expression in the form \(a+b i .\) $$ \frac{4-\sqrt{-8}}{2} $$

Simplify each exponential expression. $$ \left(-14 a^{5} b c^{2}\right)\left(2 a b c^{4}\right) $$

The number of cellular telephone subscribers in the United States from 1995 through 2009 can be modeled by \(f(x)=17 x^{16 / 15},\) where y is the number of cellular telephone subscriptions in millions, \(x\) years after \(1995 .\) (Source: Based on data from CTIA-The Wireless Association, 1995-2009) Use this information to answer Exercises 97 and 98. Predict the number of cellular telephone subscriptions in 2012. Round to the nearest tenth of a million.

Find the midpoint of each line segment whose endpoints are given. (-4.6,2.1)\(;(-6.7,1.9)\)

Write each expression in the form \(a+b i .\) $$ \frac{5-\sqrt{-75}}{10} $$

Simplify each exponential expression. $$ \frac{7 x^{-1} y}{14\left(x^{5} y^{2}\right)^{-2}} $$

Explain how writing \(x^{-7}\) with positive exponents is similar to writing \(x^{-1 / 4}\) with positive exponents.

Perform each indicated operation. \(6 x+8 x\)

Describe how to find the conjugate of a complex number.

Simplify each exponential expression. $$ \frac{\left(2 a^{-1} b^{2}\right)^{3}}{\left(8 a^{2} b\right)^{-2}} $$

Explain how writing \(2 x^{-5}\) with positive exponents is similar to writing \(2 x^{-3 / 4}\) with positive exponents.

Perform each indicated operation. \((6 x)(8 x)\)

Explain why the product of a complex number and its complex conjugate is a real number.

Which of the following are not real numbers? $$ \sqrt{-17} $$

Fill in each box with the correct expression. $$ \square \cdot a^{2 / 3}=a^{3 / 3}, \text { or } a $$

Perform each indicated operation. \((2 x+3)(x-5)\)

Simplify. $$ (8-\sqrt{-3})-(2+\sqrt{-12}) $$

Fill in each box with the correct expression. $$ \square \cdot x^{1 / 8}=x^{4 / 8}, \text { or } x^{1 / 2} $$

Perform each indicated operation. \((2 x+3)+(x-5)\)

Which of the following are not real numbers? $$ \sqrt[3]{-17} $$

Simplify. $$ (8-\sqrt{-4})-(2+\sqrt{-16}) $$

Which of the following are not real numbers? $$ \sqrt[10]{-17} $$

Fill in each box with the correct expression. $$ \frac{\square}{x^{-2 / 5}}=x^{3 / 5} $$

Perform each indicated operation. \(9 y^{2}-8 y^{2} \quad\)

Perform each indicated operation. $$ 9 y^{2}-8 y^{2} $$

Determine whether \(2 i\) is a solution of \(x^{2}+4=0\).

Which of the following are not real numbers? $$ \sqrt[15]{-17} $$

Perform each indicated operation. \(\left(9 y^{2}\right)\left(-8 y^{2}\right) \quad\)

Determine whether \(-1+i\) is a solution of \(x^{2}+2 x=-2\)

$$ \text { Explain why } \sqrt{-64} \text { is not a real number. } $$

Use a calculator to write a four-decimal-place approximation of each number. $$ 8^{1 / 4} $$

Perform each indicated operation. \((x-4)^{2} \quad\)

Perform each indicated operation. $$ (x-4)^{2} $$

$$ \text { Explain why } \sqrt[3]{-64} \text { is a real number. } $$

Use a calculator to write a four-decimal-place approximation of each number. $$ 18^{3 / 5} $$

Perform each indicated operation. \((2 x+1)^{2}\)

Do not use a calculator. \(\sqrt{160}\) is closest to a. 10 b. \(13 \quad\) c. 20 d. 40

In physics, the speed of a wave traveling over a stretched string with tension \(t\) and density \(u\) is given by the expression \(\frac{\sqrt{t}}{\sqrt{u}}\). Write this expression with rational exponents.