6.7 Integer exponents and scientific notation  (Page 6/10)

ⓐ $4^{\mathrm{-2}}$
ⓑ ${10}^{\mathrm{-3}}$

ⓐ $3^{\mathrm{-4}}$
ⓑ ${10}^{\mathrm{-2}}$

ⓐ $5^{-3}$
ⓑ ${10}^{\mathrm{-5}}$

ⓐ $2^{\mathrm{-8}}$
ⓑ ${10}^{\mathrm{-2}}$

ⓐ $\frac{1}{c^{\mathrm{-5}}}$
ⓑ $\frac{1}{3^{\mathrm{-2}}}$

ⓐ $\frac{1}{c^{\mathrm{-5}}}$
ⓑ $\frac{1}{5^{\mathrm{-2}}}$

ⓐ $\frac{1}{q^{\mathrm{-10}}}$
ⓑ $\frac{1}{{10}^{\mathrm{-3}}}$

ⓐ $\frac{1}{t^{\mathrm{-9}}}$
ⓑ $\frac{1}{{10}^{\mathrm{-4}}}$

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

ⓐ ${\left(\frac{3}{10}\right)}^{\mathrm{-2}}$
ⓑ ${\left(-\frac{2}{cd}\right)}^{\mathrm{-3}}$

ⓐ ${\left(\frac{4}{9}\right)}^{\mathrm{-3}}$
ⓑ ${\left(-\frac{u^2}{2v}\right)}^{\mathrm{-5}}$

ⓐ ${\left(\frac{7}{2}\right)}^{\mathrm{-3}}$
ⓑ ${\left(-\frac{3}{x{y}^2}\right)}^{\mathrm{-3}}$

ⓐ ${\left(-5\right)}^{-2}$
ⓑ $\text{−}{5}^{\mathrm{-2}}$
ⓒ ${\left(-\frac{1}{5}\right)}^{\mathrm{-2}}$
ⓓ $\text{−}{\left(\frac{1}{5}\right)}^{\mathrm{-2}}$

ⓐ ${\left(\mathrm{-7}\right)}^{\mathrm{-2}}$
ⓑ $-7^{-2}$
ⓒ ${\left(-\frac{1}{7}\right)}^{\mathrm{-2}}$
ⓓ $\text{−}{\left(\frac{1}{7}\right)}^{\mathrm{-2}}$

ⓐ $\text{−}{3}^{\mathrm{-3}}$
ⓑ ${\left(-\frac{1}{3}\right)}^{\mathrm{-3}}$
ⓒ $\text{−}{\left(\frac{1}{3}\right)}^{\mathrm{-3}}$
ⓓ ${\left(\mathrm{-3}\right)}^{\mathrm{-3}}$

ⓐ $\text{−}{5}^{\mathrm{-3}}$
ⓑ ${\left(-\frac{1}{5}\right)}^{\mathrm{-3}}$
ⓒ $\text{−}{\left(\frac{1}{5}\right)}^{\mathrm{-3}}$
ⓓ ${\left(\mathrm{-5}\right)}^{\mathrm{-3}}$

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

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

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

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

ⓐ $m^{\mathrm{-4}}$
ⓑ ${\left(x^3\right)}^{\mathrm{-4}}$

ⓐ $b^{\mathrm{-5}}$
ⓑ ${\left(k^2\right)}^{\mathrm{-5}}$

ⓐ $p^{\mathrm{-10}}$
ⓑ ${\left(q^6\right)}^{\mathrm{-8}}$

ⓐ $s^{\mathrm{-8}}$
ⓑ ${\left(a^9\right)}^{\mathrm{-10}}$

ⓐ $7n^{\mathrm{-1}}$
ⓑ ${(7n)}^{\mathrm{-1}}$
ⓒ ${(\mathrm{-7}n)}^{\mathrm{-1}}$

ⓐ $6r^{\mathrm{-1}}$
ⓑ ${(6r)}^{\mathrm{-1}}$
ⓒ ${(\mathrm{-6}r)}^{\mathrm{-1}}$

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

ⓐ ${\left(2q\right)}^{\mathrm{-4}}$
ⓑ $2q^{\mathrm{-4}}$
ⓒ $\mathrm{-2}{q}^{\mathrm{-4}}$

ⓐ $b^4{b}^{\mathrm{-8}}$
ⓑ $r^{\mathrm{-2}}{r}^5$
ⓒ $x^{\mathrm{-7}}{x}^{\mathrm{-3}}$

ⓐ $s^3·s^{\mathrm{-7}}$
ⓑ $q^{\mathrm{-8}}·q^3$
ⓒ $y^{\mathrm{-2}}·y^{\mathrm{-5}}$

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

ⓐ $y^5·y^{\mathrm{-5}}$
ⓑ $y·y^5$
ⓒ $y·y^{\mathrm{-5}}$

$p^5·p^{\mathrm{-2}}·p^{\mathrm{-4}}$

$x^4·x^{\mathrm{-2}}·x^{\mathrm{-3}}$

$\left(w^4{x}^{\mathrm{-5}}\right)\left(w^{\mathrm{-2}}{x}^{\mathrm{-4}}\right)$

$\left(m^3{n}^{\mathrm{-3}}\right)\left(m^{\mathrm{-5}}{n}^{\mathrm{-1}}\right)$

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

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

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

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

$\left(\mathrm{-4}{r}^{\mathrm{-2}}{s}^{\mathrm{-8}}\right)\left(9r^4{s}^3\right)$

$\left(\mathrm{-5}{m}^4{n}^6\right)\left(8m^{\mathrm{-5}}{n}^{\mathrm{-3}}\right)$

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

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

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

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

$\frac{t^9}{t^{\mathrm{-3}}}$

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

$\frac{x^{\mathrm{-7}}}{x^{\mathrm{-3}}}$

$\frac{y^{\mathrm{-5}}}{y^{\mathrm{-10}}}$

57,000

340,000

8,750,000

1,290,000

0.026

0.041

0.00000871

0.00000103

$5.2\times {10}^2$

$8.3\times {10}^2$

$7.5\times {10}^6$

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

$2.5\times {10}^{\mathrm{-2}}$

$3.8\times {10}^{\mathrm{-2}}$

$4.13\times {10}^{\mathrm{-5}}$

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

$\left(3\times {10}^{\mathrm{-5}}\right)\left(3\times {10}^9\right)$

$\left(2\times {10}^2\right)\left(1\times {10}^{\mathrm{-4}}\right)$

$\left(7.1\times {10}^{\mathrm{-2}}\right)\left(2.4\times {10}^{\mathrm{-4}}\right)$

$\left(3.5\times {10}^{\mathrm{-4}}\right)\left(1.6\times {10}^{\mathrm{-2}}\right)$

$\frac{7\times {10}^{\mathrm{-3}}}{1\times {10}^{\mathrm{-7}}}$

$\frac{5\times {10}^{\mathrm{-2}}}{1\times {10}^{\mathrm{-10}}}$

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

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

The population of the United States on July 4, 2010 was almost 310,000,000. Write the number in scientific notation.

The population of the world on July 4, 2010 was more than 6,850,000,000. Write the number in scientific notation

The average width of a human hair is 0.0018 centimeters. Write the number in scientific notation.

The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.

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

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

The concentration of carbon dioxide in the atmosphere is $3.9\times {10}^{\mathrm{-4}}$ . Convert this number to decimal form.

The width of a proton is $1\times {10}^{\mathrm{-5}}$ of the width of an atom. Convert this number to decimal form.

Health care costs The Centers for Medicare and Medicaid projects that consumers will spend more than $4 trillion on health care by 2017.

1. ⓐ Write 4 trillion in decimal notation.
2. ⓑ Write 4 trillion in scientific notation.