Algebra 1 / Unit 7: Exponents and Exponential Functions
7.1 Properties of Exponents
Notes
An exponent shows repeated multiplication: $x^4 = x \cdot x \cdot x \cdot x$.
- Product rule: $x^a \cdot x^b = x^{a+b}$
- Quotient rule: $\displaystyle \frac{x^a}{x^b} = x^{a-b}$
- Power of a power: $(x^a)^b = x^{ab}$
- Power of a product: $(xy)^a = x^ay^a$
- Multiply coefficients normally: $(3x^2)(4x^5) = 12x^7$.
Practice
Simplify $x^3 \cdot x^6$.
Add exponents when multiplying the same base.
Simplify $(2a^3)^4$.
$2^4 = 16$ and $(a^3)^4 = a^{12}$.
Simplify $\displaystyle \frac{15y^8}{3y^2}$.
$15 \div 3 = 5$ and $8 - 2 = 6$.
Ready for more? Take the Unit 7 test.