Exponents with negative fractional bases

The  exercise appears under the 7th grade (U.S.) Math Mission. This exercise performs exponentiation on negative numbers and on fractions.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the power of the number: This problem provides an exponential expression with a negative fraction in the base, possibly a mixed number. The student is expected to evaluate the expression and write the answer as a simplified fraction in the space provided.Expwithfracbase1.png

Strategies
Knowledge of exponentiation and experience with switching between mixed numbers and improper fractions are encouraged to ensure success on this exercise.
 * 1) Changing a mixed number a+b/c into an improper fraction is performed by calculating ((ac+b)/c), essentially combining the two numbers with a common denominator.
 * 2) The problem can be performed on a calculator but special care needs to be taken with parentheses.

Real-life Applications

 * 1) Mixed numbers are used in common speak, for example "one and a half sodas" is more common than "three halves of a soda."
 * 2) Exponent rules come up in many contexts, for example, as an aid to remembering the logarithmic properties and rules.