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Exponents: sub-module 4 of 6 of math tutorials

An exponent, also known as a power, indicates repeated multiplication of the same quantity. For example, we can write 2∙2∙2∙2 in exponential notation as 24 to the power of 4, where 2 is the base and 4 is the exponent (or power). We can read this as 2 to the fourth power or 2 to the power of 4. This module will review the exponent rules that can be used to simplify expressions containing exponents and how to use scientific notation to write very large or very small numbers.


Top Tips

  • Use the properties of exponents to simplify expressions that contain exponents. To multiply exponents with the same base, ADD the exponents. To divide exponents with the same base, SUBTRACT the exponents. To raise an exponent to another exponent, MULTIPLY the exponents.
  • Pay close attention to signs and parentheses. For example, (-3x)2, -(3x)2 and -3x2 are ALL different!
  • Express negative exponents as positive exponents in your final answer. A negative exponent can be expressed as a positive exponent by writing the reciprocal and changing the sign of the exponent.
  • Any number or variable raised to the power of zero is 1. It doesn’t matter what the base is, ANYTHING with an exponent of zero is ALWAYS equal to 1.
  • Use scientific notation to write very large or very small numbers in a shorter way. The exponent on the factor of 10 is positive when the number is large (greater than 1), and negative when the number is small (between 0 and 1). The value of the exponent tells us how many places to move the decimal.
  • When doing operations with numbers in scientific notation, keep them in scientific notation. Use exponent rules to simplify the expression, and write the final answer in scientific notation.
  • Make sure your answers are written correctly in scientific notation. In correct scientific notation, the first factor must have the decimal placed directly to the right of the first non-zero digit, and the second factor is 10 raised to a power.