Quotient of Powers Property - Same Base
The Quotient of Powers Property for the same base is a Grade 7 exponent rule in Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation. When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator: a^m divided by a^n equals a^(m-n). For example, y^10 divided by y^4 equals y^6.
Key Concepts
If $a$ is a real number, $a \neq 0$, and $m$ and $n$ are positive integers, then $$\frac{a^m}{a^n} = a^{m n}$$.
Common Questions
What is the Quotient of Powers Property?
The Quotient of Powers Property states that when dividing two powers with the same base, subtract the exponents: a^m divided by a^n equals a^(m minus n).
How do you simplify x^8 divided by x^2?
Use the Quotient of Powers Property: subtract the exponents to get x^(8 minus 2) equals x^6.
Why does the Quotient of Powers Property work?
When you divide powers of the same base, common factors in the numerator and denominator cancel out. For example, x^5 divided by x^2 cancels two x factors from both top and bottom, leaving x^3.
What textbook covers the Quotient of Powers Property in Grade 7?
Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation covers the Quotient of Powers Property and other exponent rules.