Section P.3 Homework

1. Is there a difference between (−4)⁴ and −4⁴?

2.  When we multiply two powers with the same base, we ______ the exponents. So 5⁴ · 5⁷ =

3.  Express the following numbers without using exponents.

$$\begin{gathered} A. 2^{–1} \\ B. 2^{–3} \\ C. \frac{1^{–1}}{2} \\ D. \frac{1}{2^{–3}} \end{gathered}$$

4.   Evaluate each expression.

$$\begin{gathered} A. {\left(\frac{2}{3}\right)}^0·2^{–2} \\ B. \frac{3^{–2}}{5^0} \\ C. {\left(\frac{1}{5}\right)}^{–2} \end{gathered}$$

5.  Simplify each expression.

$$\begin{gathered} A. y^4·y^{–7} \\ B. z^6{z}^{–3}{z}^{–5} \\ c.\frac{x^6}{x^{10}} \end{gathered}$$

6. Simplify each expression.

$$\begin{gathered} A. \frac{z^2{z}^4}{z^3{z}^{–1}} \\ B. {\left(2a^2{a}^4\right)}^3 \\ C.{\left(–3z^2\right)}^3\left(4z^4\right) \end{gathered}$$

7.  Simplify each expression, and eliminate any negative exponent(s).

$$\begin{gathered} A. \left(5x^3{y}^2\right)\left(7y^7\right) \\ B. \left(6y^{–2}{z}^5\right)\left(9y^{3}z\right) \\ C. \left(8x^7{y}^2\right){\left(\frac{1}{2}{x}^{3}y\right)}^{–2} \end{gathered}$$

8.  Simplify each expression, and eliminate any negative exponent(s).

$$\begin{gathered} A. {\left(\frac{s^6{t}^{–5}}{3s^{–1}t}\right)}^{–2} \\ B. {\left(\frac{x{y}^{–5}{z}^{–4}}{x^2{y}^5{z}^{–7}}\right)}^{–3} \end{gathered}$$

9.  Write each number in scientific notation.

1. 139,540,000
2. 7,397,000,000
3. 0.0000000019
4. 0.0007475

10.  Write each number in decimal notation.

1. 7.2 × 10¹⁴
2. 6 × 10¹²
3. 8.54 × 10⁻³
4. 6.257 × 10⁻⁸

11.  Write the number indicated in each statement in scientific notation.

(a) The distance from the earth to the sun is about 93 million miles.

(b) The mass of an oxygen molecule is about 0.000000000000000000000053 g.

(c) The mass of the earth is about 5,970,000,000,000,000,000,000,000 kg.

12. Use scientific notation, the Laws of Exponents, and a calculator to perform the indicated operation. State your answer rounded to the number of significant digits indicated by the given data.

(7.7 × 10⁻²)(1.805 × 10⁻¹⁵)

13.  The speed of light is about 186,000 mi/s. The distance from the earth to the sun is about 93 million miles. Use this information to find how long it takes for a light ray from the sun to reach the earth. (Round your answer to two decimal places.)

14.  A sealed room in a hospital, measuring 4 m wide, 10 m long, and 3 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains 6.02  10²³ molecules (Avogadro’s number). How many molecules of oxygen are there in the room? (Enter your answer in scientific notation. Round the decimal value to two decimal places.)

15.   If you had ten million (10⁷) dollars in a suitcase and you spent ten thousand (10⁴) dollars each day, how many years would it take you to use all the money? (Round your answer to two decimal places. Consider a year to have exactly 365 days.)

If you spent at the same rate, how many years would it take you to empty a suitcase filled with a billion (10⁹) dollars? (Round your answer to two decimal places. Consider a year to have exactly 365 days.)