1.2 Exponents and scientific notation  (Page 8/9)

Is $2^3$ the same as $3^2?$ Explain.

When can you add two exponents?

What is the purpose of scientific notation?

Explain what a negative exponent does.

$9^2$

${15}^{\mathrm{-2}}$

$3^2\times 3^3$

$4^4÷4$

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

${(5-8)}^0$

${11}^3÷{11}^4$

$6^5\times 6^{\mathrm{-7}}$

${\left(8^0\right)}^2$

$5^{\mathrm{-2}}÷5^2$

$4^2\times 4^3÷4^{\mathrm{-4}}$

$\frac{6^{12}}{6^9}$

${\left({12}^3\times 12\right)}^{10}$

${10}^6÷{\left({10}^{10}\right)}^{\mathrm{-2}}$

$7^{\mathrm{-6}}\times 7^{\mathrm{-3}}$

${\left(3^3÷3^4\right)}^5$

0.0000314

148,000,000

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

$9.8\times {10}^{\mathrm{-9}}$

$\frac{a^3{a}^2}{a}$

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

${\left(b^3{c}^4\right)}^2$

${\left(\frac{x^{\mathrm{-3}}}{y^2}\right)}^{\mathrm{-5}}$

$a{b}^2÷d^{\mathrm{-3}}$

${\left(w^0{x}^5\right)}^{\mathrm{-1}}$

$\frac{m^4}{n^0}$

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

$\frac{p^{\mathrm{-4}}{q}^2}{p^2{q}^{\mathrm{-3}}}$

${(l\times w)}^2$

${\left(y^7\right)}^3÷x^{14}$

${\left(\frac{a}{2^3}\right)}^2$

$5^{2}m÷5^{0}m$

$\frac{{\left(16\sqrt{x}\right)}^2}{y^{\mathrm{-1}}}$

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

${\left(m{a}^6\right)}^2\frac{1}{m^3{a}^2}$

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

${\left(x^2{y}^{13}÷y^0\right)}^2$

${\left(9z^3\right)}^{\mathrm{-2}}y$

To reach escape velocity, a rocket must travel at the rate of $2.2\times {10}^6$ ft/min. Rewrite the rate in standard notation.

A dime is the thinnest coin in U.S. currency. A dime’s thickness measures $2.2\times {10}^6$ m. Rewrite the number in standard notation.

The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.

A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.

The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was $\text{\$}1.71496\times {10}^{13}.$ Rewrite the GDP in standard notation.

One picometer is approximately $3.397\times {10}^{\mathrm{-11}}$ in. Rewrite this length using standard notation.

The value of the services sector of the U.S. economy in the first quarter of 2012 was $10,633.6 billion. Rewrite this amount in scientific notation.

${\left(\frac{{12}^3{m}^{33}}{4^{\mathrm{-3}}}\right)}^2$

${17}^3÷{15}^2{x}^3$

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

${\left(6^2\mathrm{-24}\right)}^2÷{\left(\frac{x}{y}\right)}^{\mathrm{-5}}$

$\frac{m^2{n}^3}{a^2{c}^{\mathrm{-3}}}\cdot \frac{a^{\mathrm{-7}}{n}^{\mathrm{-2}}}{m^2{c}^4}$

${\left(\frac{x^6{y}^3}{x^3{y}^{\mathrm{-3}}}\cdot \frac{y^{\mathrm{-7}}}{x^{\mathrm{-3}}}\right)}^{10}$

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

Avogadro’s constant is used to calculate the number of particles in a mole. A mole is a basic unit in chemistry to measure the amount of a substance. The constant is $6.0221413\times {10}^{23}.$ Write Avogadro’s constant in standard notation.

Planck’s constant is an important unit of measure in quantum physics. It describes the relationship between energy and frequency. The constant is written as $6.62606957\times {10}^{\mathrm{-34}}.$ Write Planck’s constant in standard notation.