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Study Guides > Intermediate Algebra

Why It Matters: Exponents

Artist's concept of Voyager in flight. Artist's concept of Voyager in flight.
Mathematicians, scientists, and economists commonly encounter very large and very small numbers.  For example, Star Wars fans may remember Han Solo bragging about the Millennium Falcon's ability to make the Kessel Run in less than 1212 parsecs in Episode IV.  He was referring to a smuggler's route with sections that were flown in hyperspace, making length an important factor in how quickly a ship could make the run. In reality, a parsec is a unit of length used to measure large distances to objects outside the solar system. A parsec is equal to about 3131 trillion kilometers, or 1919 trillion miles in length. Rather than writing all the zeros associated with the number 11 trillion (1,000,000,000,000)(1,000,000,000,000) we commonly use the written words or scientific notation. Scientific notation uses exponents to represent the number of zeros that come before or after the important digits of a very small or large number. Using scientific notation, 1919 trillion miles would be written 1.9×1013{1.9}\times{10}^{13} miles. The most distant space probe, Voyager 11, was 0.00060.0006 parsecs from Earth as of March 20152015. It took Voyager 3737 years to cover that distance. Voyager 1 was launched by NASA on September 5,19775, 1977. As of 20132013, the probe was moving with a relative velocity to the sun of about 1703017030 m/s. With the velocity the probe is currently maintaining, Voyager 11 is traveling about 325325 million miles per year, or 520520 million kilometers per year. Here are some more distances to well-known astronomical objects in parsecs:
  • The distance to the open cluster Pleiades is 130130 parsecs from Earth. That's 1.7×1015{1.7}\times{10}^{15} miles.
  • The center of the Milky Way is more than 88 kiloparsecs (a kiloparsec is 10001000 parsecs) from Earth, and the Milky Way is roughly 3434 kiloparsecs across.
  • The nearest star to Earth, Proxima Centauri, is about 1.31.3 parsecs from the sun.
  • Most of the stars visible to the unaided eye in the nighttime sky are within 500500 parsecs of the sun.
In this section, you will learn the rules for algebraic operations on terms with exponents, then apply them to calculations involving very large or small numbers.

Learning Outcomes

  • Apply exponent rules to simplify expressions with integer exponents
  • Write very large and very small numbers in scientific notation
  • Apply exponent rules to numbers written in scientific notation in applications

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