Can you simplify the following expression so that it has only positive exponents?
James Sousa: Simplify Exponential Expressions
The following table summarizes all of the rules for exponents.
Laws of Exponents
If a∈R,a≥0 and m,n∈Q, then
- aman=am−n (if m>n,a≠0)
- (ab)n=anbn (b≠0)
- a0=1 (a≠0)
Solution: First, rewrite with a positive exponent:
Next, evaluate the fractional exponent:
Concept Problem Revisited
- In an algebraic expression, the base is the variable, number, product or quotient, to which the exponent refers. Some examples are: In the expression 25, ‘2’ is the base. In the expression (−3y)4, ‘−3y’ is the base.
- In an algebraic expression, the exponent is the number to the upper right of the base that tells how many times to multiply the base times itself. Some examples are:
- In the expression 25, ‘5’ is the exponent. It means to multiply 2 times itself 5 times as shown here: 25=2×2×2×2×2.
- In the expression (−3y)4, ‘4’ is the exponent. It means to multiply −3y times itself 4 times as shown here: (−3y)4=−3y×−3y×−3y×−3y.
- Laws of Exponents
- The laws of exponents are the algebra rules and formulas that tell us the operation to perform on the exponents when dealing with exponential expressions.
Use the laws of exponents to simplify each of the following:
Simplify each expression.
Express each of the following as a power of 3. Do not evaluate.
Apply the laws of exponents to evaluate each of the following without using a calculator.
Use the laws of exponents to simplify each of the following.
Simplify each of the following using the laws of exponents.
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 6.6.