Integer Exponents and Scientific Notation Summary

Key Concepts

• Property of Negative Exponents
  • If \(n\) is a positive integer and \(a\ne 0\), then \(\frac{1}{{a}^{\text{−}n}}={a}^{n}\)
• Quotient to a Negative Exponent
  • If \(a,b\) are real numbers, \(b\ne 0\) and \(n\) is an integer , then \({\left(\frac{a}{b}\right)}^{\text{−}n}={\left(\frac{b}{a}\right)}^{n}\)
• To convert a decimal to scientific notation:
  1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
  2. Count the number of decimal places, \(n\), that the decimal point was moved.
  3. Write the number as a product with a power of 10. If the original number is:
     • greater than 1, the power of 10 will be \({10}^{n}\)
     • between 0 and 1, the power of 10 will be \({10}^{\text{−}n}\)
  4. Check.
• To convert scientific notation to decimal form:
  1. Determine the exponent, \(n\), on the factor 10.
  2. Move the decimal \(n\)places, adding zeros if needed.
     • If the exponent is positive, move the decimal point \(n\) places to the right.
     • If the exponent is negative, move the decimal point \(|n|\) places to the left.
  3. Check.