# What Exponents Are: Everything You Need to Know

An exponent is a concept in mathematics that is used to represent repeated multiplication. Exponents are utilized in areas of math and science to represent very large or very small numbers in physics, chemistry, astronomy, and engineering. They can be used to describe growth of populations, decay of microchemical substances, taking measurements of objects, and earnings on investment charts. The exponent number signifies how many times the base number should be multiplied by itself. For example, in the math expression 3^{4}, 3 is the base number and 4 is the exponent. This expression written out and solved would look like the following: 3 * 3 * 3 * 3 = 81.

### Why use exponents?

Exponents are useful for writing large numbers of repeated multiplication. The notation is not only shorter but easier to read and manipulate. For instance, consider the number 1,000,000. Instead of writing 10 * 10 * 10 * 10 * 10 * 10, we can write 10^{6}.

### Rules of exponents

Exponents have a set of rules to allow us to simplify expressions, combine terms, and solve equations. Here are the basic and important rules of exponents:

Rules of One | n^{1} = n, where n is any number |

Zero Exponent | n^{0} = 1, where n is any non-zero number |

Product Rule | n^{a} * n^{b} = n^{(a+b)}, where n is any number and a and b are any integers |

Quotient Rule | n^{a}/n^{b} = n^{(a-b)}, where n is any non-zero number and a and b are any integers |

Power Rule | (n^{a})^{b} = n^{(a *} ^{b)}, where n is any number and a and be are any integers |

Power of a Product Rule | (nm)^{a} = n^{a}m^{a}, where n is any non-zero number and a and b are any integers |

Negative Exponent | n^{-a} = 1 / (n^{a}) |

Fractional Exponent | n^{a/b} = ^{b}√n^{a} |

The rules can be used to simplify expressions that involve exponents. For instance, we will use the equation: (3^{2} * 3^{4}) / 3^{3}. First, we will use the product rule, n^{a} * n^{b} = n^{(a+b)}, and simplify the numerator to 3^{(2+4)} = 3^{6}. Next, using the quotient rule, n^{a}/n^{b} = n^{(a-b)}, we simplify the numerator and denominator: 3^{6}/3^{3} = 3^{(6-3)} = 3^{3} or 9.

For a more comprehensive list of the 7 rules of exponents, click here.

### Why are exponents important?

Exponents are a powerful tool that are used to represented repeated multiplication or division. They are used to describe growth and decay, solve equations, and write large or small numbers. Understanding exponents is essential for success in many areas of mathematics and science.

For more information and practice with exponents click here.

Author: Maerie Morales

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