Where do you need or use exponents in everyday life?

Common people who are not using math in their work or anything wouldn't typically use exponents as such in normal life, since it doesn't occur that often that you'd need to calculate 7 x 7 x 7 x 7  or  0.1 x 0.1 x 0.1 x 0.1 x 0.1 or other such calculations. Exponents are more or less just a shorthand notation for multiplying the same number by itself several times - and in normal life you just don't need such often.

One example of how exponents do kind of connect with our everyday lives: when we speak about square feet, square meters, square inches, square miles, square kilometers or any other area units, or when we speak about cubic feet, cubic meters, cubic centimeters or any other such volume units.

The unit "square foot" is actually 1 foot x 1 foot, or (1 foot) squared, or (1 foot) to the power of 2. Similarly, a cubic foot is 1 foot x 1 foot x 1 foot, or (1 foot) cubed, or (1 foot) to the power of 3.

If you talk about SQUARE shaped areas, for example if you say "My room is twelve by twelve square", you're meaning your room is 12 feet x 12 feet, or 12² square feet.

Another kind of indirect example is if you talk about extremely tiny or extremely big quantities. For example, the term 'nanometer' means 10^-9 meter. The prefix 'nano' means the number 10^-9 - an extremely small number. Or, within computer world you often see megabytes, gigabytes, terabytes. "Mega" means 10⁶ or one million, "giga" means 10⁹, and "tera" means 10¹². Or megahertz - million hertz.

See also

Math. "How am I ever going to use this stuff?"A great collection of REAL-world math problems contributed by a variety of businesses, demonstrating the relevance of math in today's world. The intent of these lessons is to excite students about mathematics, to expose students to professions that employ mathematics, and to demonstrate the relevance of mathematics in solving real-world challenges.

Career profiles
Essays from authors from a variety of careers for which a background in the mathematical sciences is useful.

Examining How Mathematics is Used in the Workplace
Mathematics in Automobile Production; Proportional Reasoning by Nurses; Modeling the Mathematics of Banking; Mathematical Models as Seen by Biologists; How do Scientists Interpret Graphs?