10.5 Integer exponents and scientific notation  (Page 5/7)

$5^{\mathrm{-3}}$

$8^{\mathrm{-2}}$

$3^{\mathrm{-4}}$

$2^{\mathrm{-5}}$

$7^{\mathrm{-1}}$

${10}^{\mathrm{-1}}$

$2^{\mathrm{-3}}+2^{\mathrm{-2}}$

$3^{\mathrm{-2}}+3^{\mathrm{-1}}$

$3^{\mathrm{-1}}+4^{\mathrm{-1}}$

${10}^{\mathrm{-1}}+2^{\mathrm{-1}}$

${10}^0-{10}^{\mathrm{-1}}+{10}^{\mathrm{-2}}$

$2^0-2^{\mathrm{-1}}+2^{\mathrm{-2}}$

1. ⓐ ${(\mathrm{-6})}^{\mathrm{-2}}$
2. ⓑ $-6^{\mathrm{-2}}$

1. ⓐ ${(\mathrm{-8})}^{\mathrm{-2}}$
2. ⓑ $-8^{\mathrm{-2}}$

1. ⓐ ${(\mathrm{-10})}^{\mathrm{-4}}$
2. ⓑ $-{10}^{\mathrm{-4}}$

1. ⓐ ${(\mathrm{-4})}^{\mathrm{-6}}$
2. ⓑ $-4^{\mathrm{-6}}$

1. ⓐ $5·2^{\mathrm{-1}}$
2. ⓑ ${(5·2)}^{\mathrm{-1}}$

1. ⓐ $10·3^{\mathrm{-1}}$
2. ⓑ ${(10·3)}^{\mathrm{-1}}$

1. ⓐ $4·{10}^{\mathrm{-3}}$
2. ⓑ ${(4·10)}^{\mathrm{-3}}$

1. ⓐ $3·5^{\mathrm{-2}}$
2. ⓑ ${(3·5)}^{\mathrm{-2}}$

$n^{\mathrm{-4}}$

$p^{\mathrm{-3}}$

$c^{\mathrm{-10}}$

$m^{\mathrm{-5}}$

1. ⓐ $4x^{\mathrm{-1}}$
2. ⓑ ${(4x)}^{\mathrm{-1}}$
3. ⓒ ${(\mathrm{-4}x)}^{\mathrm{-1}}$

1. ⓐ $3q^{\mathrm{-1}}$
2. ⓑ ${(3q)}^{\mathrm{-1}}$
3. ⓒ ${(\mathrm{-3}q)}^{\mathrm{-1}}$

1. ⓐ $6m^{\mathrm{-1}}$
2. ⓑ ${(6m)}^{\mathrm{-1}}$
3. ⓒ ${(\mathrm{-6}m)}^{\mathrm{-1}}$

1. ⓐ $10k^{\mathrm{-1}}$
2. ⓑ ${(10k)}^{\mathrm{-1}}$
3. ⓒ ${(\mathrm{-10}k)}^{\mathrm{-1}}$

$p^{\mathrm{-4}}·p^8$

$r^{\mathrm{-2}}·r^5$

$n^{\mathrm{-10}}·n^2$

$q^{\mathrm{-8}}·q^3$

$k^{\mathrm{-3}}·k^{\mathrm{-2}}$

$z^{\mathrm{-6}}·z^{\mathrm{-2}}$

$a·a^{\mathrm{-4}}$

$m·m^{\mathrm{-2}}$

$p^5·p^{\mathrm{-2}}·p^{\mathrm{-4}}$

$x^4·x^{\mathrm{-2}}·x^{\mathrm{-3}}$

$a^3{b}^{\mathrm{-3}}$

$u^2{v}^{\mathrm{-2}}$

$\left(x^5{y}^{\mathrm{-1}}\right)\left(x^{\mathrm{-10}}{y}^{\mathrm{-3}}\right)$

$\left(a^3{b}^{\mathrm{-3}}\right)\left(a^{\mathrm{-5}}{b}^{\mathrm{-1}}\right)$

$\left(u{v}^{\mathrm{-2}}\right)\left(u^{\mathrm{-5}}{v}^{\mathrm{-4}}\right)$

$\left(p{q}^{\mathrm{-4}}\right)\left(p^{\mathrm{-6}}{q}^{\mathrm{-3}}\right)$

$\left(\mathrm{-2}{r}^{\mathrm{-3}}{s}^9\right)\left(6r^4{s}^{\mathrm{-5}}\right)$

$\left(\mathrm{-3}{p}^{\mathrm{-5}}{q}^8\right)\left(7p^2{q}^{\mathrm{-3}}\right)$

$\left(\mathrm{-6}{m}^{\mathrm{-8}}{n}^{\mathrm{-5}}\right)\left(\mathrm{-9}{m}^4{n}^2\right)$

$\left(\mathrm{-8}{a}^{\mathrm{-5}}{b}^{\mathrm{-4}}\right)\left(\mathrm{-4}{a}^2{b}^3\right)$

${\left(a^3\right)}^{\mathrm{-3}}$

${\left(q^{10}\right)}^{\mathrm{-10}}$

${\left(n^2\right)}^{\mathrm{-1}}$

${\left(x^4\right)}^{\mathrm{-1}}$

${\left(y^{\mathrm{-5}}\right)}^4$

${\left(p^{\mathrm{-3}}\right)}^2$

${\left(q^{\mathrm{-5}}\right)}^{\mathrm{-2}}$

${\left(m^{\mathrm{-2}}\right)}^{\mathrm{-3}}$

${\left(4y^{\mathrm{-3}}\right)}^2$

${\left(3q^{\mathrm{-5}}\right)}^2$

${\left(10p^{\mathrm{-2}}\right)}^{\mathrm{-5}}$

${\left(2n^{\mathrm{-3}}\right)}^{\mathrm{-6}}$

$\frac{u^9}{u^{\mathrm{-2}}}$

$\frac{b^5}{b^{\mathrm{-3}}}$

$\frac{x^{\mathrm{-6}}}{x^4}$

$\frac{m^5}{m^{\mathrm{-2}}}$

$\frac{q^3}{q^{12}}$

$\frac{r^6}{r^9}$

$\frac{n^{\mathrm{-4}}}{n^{\mathrm{-10}}}$

$\frac{p^{\mathrm{-3}}}{p^{\mathrm{-6}}}$

45,000

280,000

8,750,000

1,290,000

0.036

0.041

0.00000924

0.0000103

The population of the United States on July 4, 2010 was almost $\mathrm{310,000,000}.$

The population of the world on July 4, 2010 was more than $\mathrm{6,850,000,000}.$

The average width of a human hair is $0.0018$ centimeters.

The probability of winning the $2010$ Megamillions lottery is about $0.0000000057.$

$4.1\times {10}^2$

$8.3\times {10}^2$

$5.5\times {10}^8$

$1.6\times {10}^{10}$

$3.5\times {10}^{\mathrm{-2}}$

$2.8\times {10}^{\mathrm{-2}}$

$1.93\times {10}^{\mathrm{-5}}$

$6.15\times {10}^{\mathrm{-8}}$

In 2010, the number of Facebook users each day who changed their status to ‘engaged’ was $2\times {10}^4.$

At the start of 2012, the US federal budget had a deficit of more than $\text{\$1.5}\times {10}^{13}.$

The concentration of carbon dioxide in the atmosphere is $3.9\times {10}^{\mathrm{-4}}.$

The width of a proton is $1\times {10}^{\mathrm{-5}}$ of the width of an atom.

$(2\times {10}^5)(2\times {10}^{\mathrm{-9}})$

$(3\times {10}^2)(1\times {10}^{\mathrm{-5}})$

$(1.6\times {10}^{\mathrm{-2}})(5.2\times {10}^{\mathrm{-6}})$

$(2.1\times {10}^{\mathrm{-4}})(3.5\times {10}^{\mathrm{-2}})$

$\frac{6\times {10}^4}{3\times {10}^{\mathrm{-2}}}$

$\frac{8\times {10}^6}{4\times {10}^{\mathrm{-1}}}$

$\frac{7\times {10}^{\mathrm{-2}}}{1\times {10}^{\mathrm{-8}}}$

$\frac{5\times {10}^{\mathrm{-3}}}{1\times {10}^{\mathrm{-10}}}$

Calories In May 2010 the Food and Beverage Manufacturers pledged to reduce their products by $1.5$ trillion calories by the end of 2015.

1. ⓐ Write $1.5$ trillion in decimal notation.
2. ⓑ Write $1.5$ trillion in scientific notation.

Length of a year The difference between the calendar year and the astronomical year is $0.000125$ day.

1. ⓐ Write this number in scientific notation.
2. ⓑ How many years does it take for the difference to become 1 day?

Calculator display Many calculators automatically show answers in scientific notation if there are more digits than can fit in the calculator’s display. To find the probability of getting a particular 5-card hand from a deck of cards, Mario divided $1$ by $\mathrm{2,598,960}$ and saw the answer $3.848\times {10}^{\mathrm{-7}}.$ Write the number in decimal notation.

Calculator display Many calculators automatically show answers in scientific notation if there are more digits than can fit in the calculator’s display. To find the number of ways Barbara could make a collage with $6$ of her $50$ favorite photographs, she multiplied $50·49·48·47·46·45.$ Her calculator gave the answer $1.1441304\times {10}^{10}.$ Write the number in decimal notation.

1. ⓐ Explain the meaning of the exponent in the expression $2^3.$
2. ⓑ Explain the meaning of the exponent in the expression $2^{\mathrm{-3}}$

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?