Powers with Variables
Powers with variables is a Grade 7 algebra concept in Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation. When a variable is used as a base with an exponent, the same rules apply as with numerical bases: x^n means x is multiplied by itself n times. For example, x^3 equals x times x times x, and 2a^2 means 2 times a times a (the exponent applies only to a, not to the coefficient 2).
Key Concepts
Variables can be used as bases in exponential expressions. When a variable is raised to an exponent, it follows the same rules as numerical bases: $x^n$ means $x$ is multiplied by itself $n$ times.
Common Questions
What does a variable raised to a power mean?
A variable raised to a power means the variable is used as a factor that many times. For example, x^3 means x times x times x, following the same rule as numerical bases.
Does the exponent apply to the coefficient when writing 2a^2?
No, the exponent 2 applies only to the variable a, not to the coefficient 2. So 2a^2 means 2 times a times a. Parentheses are needed to apply the exponent to both: (2a)^2 means 4a^2.
How do you evaluate a power with a variable when the variable is negative?
The sign matters: (-y)^4 includes the negative sign in the base and equals a positive result. But -y^4 without parentheses means the negative applies after squaring, giving a negative result.
What textbook covers powers with variables in Grade 7?
Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation covers using variables as bases in exponential expressions.