Properties of exponents

The  exercise appears under the 8th Grade Math Mission. This exercise practices several of the exponent rules, including product rules, power rules, and rules for negative exponents.

Types of Problems
There are five types of problems in this exercise:


 * 1) Apply exponent rules: This problem provides a set of three expressions that can be simplified via exponent rules. The student is asked to fill in the blanks with the correct exponent to make true statements.Poe1.png
 * 2) Recognize the pattern: This problem has a table with various powers of a particular base. By filling in the values the student will be able to find a pattern and place it in the provided space.Poe2.png
 * 3) Write the expression: This problem has a single exponential expression that can be simplified via exponent rules. The student is expected to correctly simplify and enter the entire expression in the space provided.Poe3.png
 * 4) Select the equivalent expressions: This problem provides a particular numerical expression involving exponents. The student is asked to select all equivalent numerical expressions from a multiple select list.Poe4.png
 * 5) Select the correct interval for each value: This problem has several numerical expressions and an interval chart. The student selects the interval in which each numerical expression falls.Poe5.png

Strategies
Knowledge of the exponent rules are key to doing this exercise accurately and efficiently.
 * 1) With the same base, exponentials being multiplied causes addition of the exponents. $$(a^n*a^m=a^(n+m)) $$
 * 2) An exponential raised to a power causes multiplication in the exponent. $$ (a^n)^m=a^(nm) $$
 * 3) Exponents distribute through multiplication.
 * 4) A negative exponent implies a reciprocal. $$ a^(-1)=\frac{1}{a} $$
 * 5) In the Apply the exponent rules problem, the answer is only the exponent. In the Write the expression problem, the whole expression is required.

Real-life applications

 * 1) Exponents have application in biology (population growth and decay), chemistry and physics (decay) and business (compound interest). Furthermore, the exponent rules by themselves have direct application to problems using scientific notation.