Multiplying Three or More Factors, Exponents
Grade 4 students learn exponent notation as a shortcut for repeated multiplication in Saxon Math Intermediate 4. In an expression like 5 squared, the base is 5 and the exponent is 2, meaning 5 times 5 = 25. For 4 cubed (4 with exponent 3), the calculation is 4 times 4 times 4 = 64. Students also multiply three or more factors by pairing and multiplying in steps. A critical error is treating 4 cubed as 4 times 3 = 12 instead of 4 times 4 times 4 = 64. This Chapter 7 skill connects repeated multiplication to exponential notation and builds the foundation for algebraic expressions.
Key Concepts
New Concept An exponent is a number that shows how many times another number (the base ) is to be used as a factor. $$ \text{base} \rightarrow 5^2 \leftarrow \text{exponent} $$.
What’s next Next, you’ll apply this concept to simplify expressions and use the area formula $A = s^2$ to solve problems.
Common Questions
What is an exponent in math?
An exponent tells you how many times to multiply the base number by itself. In 5 with exponent 2, the base is 5 and the exponent is 2, meaning 5 times 5 = 25. In 4 with exponent 3, it means 4 times 4 times 4 = 64.
How do you evaluate 4 to the third power?
Write out the repeated multiplication: 4 times 4 times 4. Calculate step by step: 4 times 4 = 16, then 16 times 4 = 64. So 4 to the third power equals 64.
What is the difference between squaring and cubing a number?
Squaring (exponent 2) means multiplying the base by itself once: 5 squared = 5 times 5 = 25. Cubing (exponent 3) means multiplying by itself twice more: 5 cubed = 5 times 5 times 5 = 125.
What is the most common mistake with exponents?
Multiplying the base by the exponent instead of using the base as a factor repeatedly. For 4 with exponent 3, the wrong calculation is 4 times 3 = 12. The correct calculation is 4 times 4 times 4 = 64.
What Saxon Math chapter introduces exponents?
Multiplying three or more factors and exponents are introduced in Saxon Math Intermediate 4, Chapter 7 (Lessons 61-70), connecting repeated multiplication to exponential notation.