The Quotient Rule for Exponents
The quotient rule for exponents is a Grade 8 math skill covered in Chapter 7: Exponents and Scientific Notation. When dividing two powers with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator: a^m / a^n = a^(m-n), for m > n. This rule simplifies division of exponential expressions efficiently.
Key Concepts
To divide two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. For any non zero number $a$, and for whole numbers $m$ and $n$ where $m n$: $$\frac{a^m}{a^n} = a^{m n}$$.
Common Questions
What is the quotient rule for exponents?
When dividing powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).
What is x^7 / x^3?
x^7 / x^3 = x^(7-3) = x^4.
What is 2^8 / 2^5?
2^8 / 2^5 = 2^(8-5) = 2^3 = 8.
Where is the quotient rule for exponents taught in Grade 8?
Chapter 7: Exponents and Scientific Notation in 8th grade math.
Why does dividing powers with the same base mean subtracting exponents?
The numerator has m copies of the base as factors and the denominator has n copies. Canceling n copies from numerator and denominator leaves m-n copies.