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The Evaluating expressions with exponents exercise appears under the 6th grade (U.S.) Math Mission. This exercise requires knowledge of the basic exponentiation rules for multiplication, division and powers to find the answers to numerical expressions

Types of Problems

There is one type of problem in this exercise:

1. Evaluate the expression: This problem provides a numerical expression involving one or more of the exponent rules. The student is expected to simplify the expression and then provide the correct expression in the provided space.

Strategies

This exercise is easy to get accuracy badges with knowledge of the exponential rules. The speed badges are medium because the numbers in the exponent can be as high as three digit numbers and are not always trivial.

1. The multiplication rule for same bases is $x^n \times x^m = x^{(n+m)}$.
2. The division rule for same bases is $x^n \over x^m$$= x^{(n-m)}$.
3. The power rule for exponents is $(x^n)^m = x^{nm}$.
4. There are also distributive properties for exponentiation through multiplication and division.

Real-life Applications

1. A kind of indirect example of using exponents is when one talks 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).