Writing Equivalent Exponential Expressions
Writing Equivalent Exponential Expressions teaches Grade 6 students to rewrite exponential expressions with different bases so they share a common base, enabling direct comparison and simplification. Covered in Illustrative Mathematics Grade 6, Unit 6: Expressions and Equations, this skill is applied by expressing a larger base as a power of a smaller base and using the power of a power rule to simplify. For example, 4^3 = (2^2)^3 = 2^6, revealing that these two expressions are equal.
Key Concepts
To compare exponential expressions with different bases, you can rewrite them to have a common base. This is often done by expressing a larger base as a power of a smaller base. The power of a power rule, $(b^m)^n = b^{m \cdot n}$, is then used to simplify the expression.
Common Questions
How do you write equivalent exponential expressions?
Rewrite one or both bases as a power of a common base, then apply the power of a power rule to combine the exponents.
How do you show that 4^3 equals 2^6?
Rewrite 4 as 2^2: then 4^3 = (2^2)^3 = 2^(2×3) = 2^6.
Why do we need a common base to compare exponential expressions?
Exponential expressions with different bases cannot be directly compared or combined using exponent rules. A common base lets you compare exponents numerically.
Where is writing equivalent exponential expressions in Illustrative Mathematics Grade 6?
This concept is in Unit 6: Expressions and Equations of Illustrative Mathematics Grade 6.
What is the power of a power rule?
(a^m)^n = a^(mn). When a power is raised to another power, multiply the exponents.