Products with Multiple Bases
Products with Multiple Bases is a Grade 8 math skill from Big Ideas Math, Course 3, Chapter 10: Exponents and Scientific Notation. Students learn to simplify expressions containing repeated multiplication of different bases by grouping like factors and expressing each group as a power, such as rewriting x·x·y·y·y as x^2y^3. This skill builds foundational understanding of exponent rules needed for algebra and scientific notation.
Key Concepts
A product containing different repeated factors can be simplified by grouping like factors and writing each group as a power. $$ \underbrace{a \cdot a \cdot \dots \cdot a} {n \text{ factors}} \cdot \underbrace{b \cdot b \cdot \dots \cdot b} {m \text{ factors}} = a^n b^m $$.
Common Questions
How do you simplify a product with multiple different bases?
Group the identical factors together, count how many times each base appears, and write each group as a power with that count as the exponent.
What does x times x times y times y times y simplify to?
It simplifies to x^2y^3, because x appears twice and y appears three times.
Where is products with multiple bases taught in Grade 8?
This skill is covered in Big Ideas Math, Course 3, Chapter 10: Exponents and Scientific Notation as part of the Grade 8 curriculum.
Why is understanding products with multiple bases important?
It underpins all exponent rules and is essential for working with polynomials, scientific notation, and algebraic expressions in higher math.