Where do you need or use exponents in everyday life?
Exponents are simply a shorthand notation for multiplying the same number by itself several times – and in everyday life you just don't often need that, because it doesn't occur that often that you'd need to calculate 7 × 7 × 7 × 7 (which is 74) or 0.1 × 0.1 × 0.1 × 0.1 × 0.1 (which is 0.15) or other such calculations.
However, here's one example of how exponents do connect with our everyday lives: square feet, square meters, square inches, square miles, square kilometers and any other square units — and cubic feet, cubic meters, cubic centimeters plus any other cubic units actually use exponents in disguise.
The unit "square foot" is in reality 1 foot × 1 foot = (1 foot) squared = (1 foot)2. Similarly, a cubic foot is 1 foot × 1 foot × 1 foot = (1 foot) cubed = (1 foot)3.
Another example of using exponents in real life is when you calculate the area of any square. If you say "My room is twelve foot by twelve foot square", you're meaning your room is 12 feet × 12 feet — 12 feet multiplied by itself — which can be written as (12 ft)2. And that simplifies to 144 square feet.
Another kind of indirect example of using exponents is when we 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, which is an extremely small decimal number (0.000000001).
Or, within computer world we often hear about megabytes, gigabytes, and terabytes. "Mega" means 106 or one million, "giga" means 109, and "tera" means 1012. The prefixes mega- and giga- are of course used in other fields as well; one example is megahertz, which means 106 or one million hertz.
Where do you need math, square roots, or algebra?
Students often question whether they will need any math skills in real life. They probably recognize the need for simple math, such as addition and multiplication, but in middle school some students start wondering why even study certain concepts, such as square roots or integers. Then, in 8th or 9th grade, when they take algebra, many more teenagers start asking the age-old question, "Where will I ever need algebra?"