What you’ll learn
Apply quotient rule.
Key idea
Same-base division subtracts the denominator exponent; subtracting a negative is not ordinary addition of both displayed exponents.
Subtract the signed denominator exponent; base is nonzero and not one for unique exponent inference.
Worked example
Enter the exact value or ordered values in the format requested below.
Rewrite 2^(-4)÷2^(1) as 2^n. Enter exponent n.
- The common base 2 is nonzero, so division subtracts denominator exponent 1 from numerator exponent -4.
- Result exponent=-4-(1)=-5; in -4-x=-5, the missing denominator exponent is x=1.
Answer: -5
Quick Check
Evaluate a worked attempt at apply quotient rule, identify the first invalid step, and provide the correction.
Step 1 notes matching nonzero bases in 2^(-1)÷2^(-5). Step 2 adds exponents to claim 2^(-6). Locate the first invalid step and correct it.