Evaluate expressions using properties of exponents
Key Notes :
Understanding the Properties of Exponents
- Product Rule: When multiplying powers with the same base, add the exponents.
- a^m * a^n = a^(m+n)
- Quotient Rule: When dividing powers with the same base, subtract the exponents.
- a^m / a^n = a^(m-n)
- Power Rule: When raising a power to another power, multiply the exponents.
- (a^m)^n = a^(m*n)
- Zero Exponent Rule: Any nonzero number raised to the power of 0 is 1.
- a^0 = 1 (where a ≠ 0)
- Negative Exponent Rule: A nonzero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.
- a^(-n) = 1/a^n (where a ≠ 0)
Evaluating Expressions
- Identify the properties of exponents that apply.
- Apply the properties step-by-step to simplify the expression.
- Calculate the final result.
Examples:
- Simplify: (2³ * 2⁴) / 2⁵
- Apply the product rule: 2^(3+4) / 2⁵
- Apply the quotient rule: 2^(7-5)
- Simplify: 2² = 4
- Evaluate: (3⁻²) * (3⁵)
- Apply the product rule: 3^(-2+5)
- Simplify: 3³ = 27
Learn with an example
Evaluate. Write your answer as a whole number or as a simplified fraction.
56 / 54 = ________
First combine powers with the same bases.
56 / 54 = 56 – 4 Divide the 5’s, remembering to subtract the exponents
52
Now evaluate.
52 = 25
Evaluate. Write your answer as a whole number or as a simplified fraction.
129 / 127 =________
First combine powers with the same bases.
129 / 127 = 129 – 7 Divide the 12’s, remembering to subtract the exponents
= 122
Now evaluate.
122 = 144
Evaluate. Write your answer as a whole number or as a simplified fraction.
78 / 76 =________
First combine powers with the same bases.
78 / 76 = 78 – 6 Divide the 7’s, remembering to subtract the exponents
= 72
Now evaluate.
72 = 49
let’s practice!
