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Please complete the following problems:

3-11 odd, 29-33 odd, and 47

And Lucy, and the rest of you who have the same question, I know this won’t really answer *all* your questions, but consider this:

# Where do you need or use exponents in everyday life?

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 12^{2} 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 10^{6} or one million, “giga” means 10^{9}, and “tera” means 10^{12}. Or megahertz – million hertz.