Division with exponents
Key Notes :
1. Division of Powers with the Same Base
- When dividing powers with the same base, subtract the exponents.
2. Zero Exponent Rule
- Any non-zero number raised to the power of zero is equal to 1.
3. Negative Exponent Rule
- A negative exponent indicates the reciprocal of the base raised to the positive exponent.
4. Dividing Powers with Different Bases
- When the bases are different, you can only simplify the expression using the properties of each individual base.
5. Simplifying Exponential Expressions
- After simplifying exponents, always check if you can further simplify the expression by reducing the numbers.
6. Application in Algebraic Expressions
- Apply the same rules to algebraic expressions.
7. Fractional Exponents
- Fractional exponents are used to represent roots.
- When dividing expressions with fractional exponents, use the same exponent rules. Example:
Learn with an example
Simplify. Express your answer as a single term, without a denominator.
j5 / j8
Simplify.
j5 / j8 = j 5-8
Divide, remembering to subtract the exponents
= j-3
Simplify. Express your answer as a single term, without a denominator.
p7 /p2
Simplify.
p7 /p2 = p7-2
Divide, remembering to subtract the exponents
= p5
Simplify. Express your answer as a single term, without a denominator.
k10 /k12
Simplify.
k10 /k12 = k10-12
Divide, remembering to subtract the exponents
= k-2
Let’s practice!🖊️
