When using the quotient power property, what result is expected?

When using the quotient power property, what result is expected?

• A. The base remains the same
• B. The exponents must be multiplied
• C. The exponents are ignored
• D. The base changes

Answer: (A)

When applying the quotient power property in exponents, the relevant rule states that when you are dividing two expressions with the same base, you subtract the exponents. This means that the base itself remains unchanged while the exponents are manipulated based on the operation being performed. For example, if you have a situation like \( a^m / a^n \), according to the quotient power property, this simplifies to \( a^{m-n} \). Here, the base \( a \) remains the same, as only the exponents \( m \) and \( n \) are involved in the calculation. Thus, the expectation that the base remains the same during this process is accurate and aligns with the rules of exponents.

When applying the quotient power property in exponents, the relevant rule states that when you are dividing two expressions with the same base, you subtract the exponents. This means that the base itself remains unchanged while the exponents are manipulated based on the operation being performed.

For example, if you have a situation like ( a^m / a^n ), according to the quotient power property, this simplifies to ( a^{m-n} ). Here, the base ( a ) remains the same, as only the exponents ( m ) and ( n ) are involved in the calculation.

Thus, the expectation that the base remains the same during this process is accurate and aligns with the rules of exponents.